Mrs. Tandy paid a $50 registration fee to join Fitness Club. She pays a monthly rate of $25. Write an equation to represent the total Mrs. Tandy pays for Fitness Club for x months. Determine if the equation you wrote represents a proportional relationship or non proportional relationship. Explain your reasoning.

Answer: r = 1/9

Step-by-step explanation:

y = rx  -->  [tex]r=\dfrac{y}{x}[/tex]

[tex]1)\ y=1\dfrac{2}{9}\rightarrow\dfrac{11}{9}\\\\.\quad x=11\\\\r=\dfrac{11}{9}\div11\\\\\\r=\dfrac{11}{9}\times \dfrac{1}{11}\quad =\large\boxed{r=\dfrac{1}{9}}[/tex]

[tex]2)\ y=2\dfrac{1}{3}\rightarrow\dfrac{7}{3}\\\\.\quad x=21\\\\r=\dfrac{7}{3}\div21\\\\\\r=\dfrac{7}{3}\times \dfrac{1}{21}\quad =\large\boxed{r=\dfrac{1}{9}}[/tex]

[tex]3)\ y=5\\\\.\quad x=45\\\\r=5\div45\\\\\\r=\dfrac{5}{45}\quad =\large\boxed{r=\dfrac{1}{9}}[/tex]

Answer:

3/128 or 0.023 units

Step-by-step explanation:

Initial amount= 3 units

Rate of change= 1/2 times a day

Amount of material at the end of day 7= 3*(1/2)^7= 3/128 ≈ 0.023 units

Answer:

3/128

Step-by-step explanation:

3x(1/2)^7=3/128

Answer:

a [tex]\mathbf{P(X=3)=0.1406}[/tex]

b [tex]\mathbf{\[P\left( {X = 3 \ or \ 4 } \right) = 0.1025}[/tex]

c  [tex]\mathbf{\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = 0.1035}[/tex]

Step-by-step explanation:

Given that:

In a multiple choice quiz:

there are 5 questions

and 4 choices for each question (a, b, c, d)

let X be the correctly answered question = 1 answer only

and Y be the choices for each question = 4 choices

The probability that Robin guessed the correct answer is:

Probability = n(X)/n(Y)

Probability = 1//4

Probability = 0.25

The probability mass function is :

[tex]P(X=x)=0.25 (1-0.25)^{x-1}[/tex]

We are to find the required probability that the first question she gets right is the 3rd question.

i.e when x = 3

[tex]P(X=3)=0.25 (1-0.25)^{3-1}[/tex]

[tex]P(X=3)=0.25 (0.75)^{2}[/tex]

[tex]\mathbf{P(X=3)=0.1406}[/tex]

b) Find the probability that  She gets exactly 3 or exactly 4 questions right

we know that :

n = 5 questions

Probability P =0.25

Let represent X to be the number of questions guessed correctly i,e 3 or 4

Then; the probability mass function can be written as:

[tex]\[P\left( {X = x} \right) = \left( {\begin{array}{*{20}{c}}\\5\\\\x\\\end{array}} \right){\left( {0.25} \right)^x}{\left( {1 - 0.25} \right)^{5 - x}}\][/tex]

[tex]P(X = 3 \ or \ 4)= P(X =3) +P(X =4)[/tex]

[tex]\[P\left( {X = 3 \ or \ 4 } \right) = \left( {\begin{array}{*{20}{c}}\\5\\\\3\\\end{array}} \right){\left( {0.25} \right)^3}{\left( {1 - 0.25} \right)^{5 - 3}}\] + \left( {\begin{array}{*{20}{c}}\\5\\\\4\\\end{array}} \right){\left( {0.25} \right)^4}{\left( {1 - 0.25} \right)^{5 - 4}}\][/tex]

[tex]\[P\left( {X = 3 \ or \ 4 } \right) = \dfrac{5!}{3!(5-3)!}\right){\left( {0.25} \right)^3}{\left( {1 - 0.25} \right)^{5 - 3}}\] + \dfrac{5!}{4!(5-4)!} \right){\left( {0.25} \right)^4}{\left( {1 - 0.25} \right)^{5 - 4}}\][/tex]

[tex]\[P\left( {X = 3 \ or \ 4 } \right) = \dfrac{5!}{3!(2)!}\right){\left( {0.25} \right)^3}{\left( {0.75} \right)^{2}}\] + \dfrac{5!}{4!(1)!} \right){\left( {0.25} \right)^4}{\left( {0.75} \right)^{1}}\][/tex]

[tex]\[P\left( {X = 3 \ or \ 4 } \right) = 0.0879+0.0146[/tex]

[tex]\mathbf{\[P\left( {X = 3 \ or \ 4 } \right) = 0.1025}[/tex]

c) Find the probability if She gets the majority of the questions right.

We know that the probability mass function is :

[tex]\[P\left( {X = x} \right) = \left( {\begin{array}{*{20}{c}}\\5\\\\x\\\end{array}} \right){\left( {0.25} \right)^x}{\left( {1 - 0.25} \right)^{5 - x}}\][/tex]

So; of She gets majority of her answers right ; we have:

The required probability is,

[tex]P(X>2) = P(X=3) +P(X=4) + P(X=5)[/tex]

∴

[tex]\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = \left( {\begin{array}{*{20}{c}}\\5\\\\3\\\end{array}} \right){\left( {0.25} \right)^3}{\left( {1 - 0.25} \right)^{5 - 3}}\] + \left( {\begin{array}{*{20}{c}}\\5\\\\4\\\end{array}} \right){\left( {0.25} \right)^4}{\left( {1 - 0.25} \right)^{5 - 4}}\]+ \left( {\begin{array}{*{20}{c}}\\5\\\\5\\\end{array}} \right){\left( {0.25} \right)^5}{\left( {1 - 0.25} \right)^{5 - 5}}\][/tex]

[tex]\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = \dfrac{5!}{3!(5-3)!}\right){\left( {0.25} \right)^3}{\left( {1 - 0.25} \right)^{5 - 3}}\] + \dfrac{5!}{4!(5-4)!} \right){\left( {0.25} \right)^4}{\left( {1 - 0.25} \right)^{5 - 4}}\] + \dfrac{5!}{5!(5-5)!} \right){\left( {0.25} \right)^5}{\left( {1 - 0.25} \right)^{5 - 5}}\][/tex]

[tex]\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = \dfrac{5!}{3!(5-3)!}\right){\left( {0.25} \right)^3}{\left( {1 - 0.75} \right)^{2}}\] + \dfrac{5!}{4!(5-4)!} \right){\left( {0.25} \right)^4}{\left( {0.75} \right)^{1}}\] + \dfrac{5!}{5!(5-5)!} \right){\left( {0.25} \right)^5}{\left( {0.75} \right)^{0}}\][/tex]

[tex]\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = 0.0879 + 0.0146 + 0.001[/tex]

[tex]\mathbf{\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = 0.1035}[/tex]

Answer:

It is AA

Step-by-step explanation:

Answer:

Option A is the right option.

Step-by-step explanation:

Sum of angles in triangle= 180°

[tex]85 + 53 + m < a = 180 \\ or \: 138 + m < a = 180 \\ or \:m < a = 180 - 138 \\ m < a = 42[/tex]

Applying sine rule:

[tex] \frac{sin \: a \: }{a} = \frac{sin \: b}{b} = \frac{sin \: c}{c} \\ \frac{sin \: b}{b} = \frac{sin \: c}{c} \\ \frac{sin \: (85)}{b} = \frac{sin(42)}{85} \\ 85 \: sin \: (85) = \: b \: sin \: (42) \\ b = \frac{85 \: sin \: (85)}{sin \: 42} \\ ac = 126.6[/tex]

Hope this helps....

Good luck on your assignment...

Answer: 8 & 13

Step-by-step explanation:

13 squared is 169 and 8 squared is 64, and the difference of those two squares would be 169 - 64 = 105. Hope this helps!

Answer:

Step-by-step explanation:

The total number of ratio units is 5+4 = 9, so each of them represents ...

  (54 g)/9 = 6 g

of fruit. Multiplying the ratio by this value shows you the amount of each kind of fruit:

  strawberry : blueberry = 5 : 4 = 5(6 g) : 4(6 g)

  strawberry : blueberry = 30 g : 24 g

There are 30 g of strawberry and 24 g of blueberry in the smoothie.

Answer: 13

Step-by-step explanation:

I used Pythagorean theorem to solve this problem. As DC and AD is 12 and 5, you would do 12²+5²= c². 12²= 144 and 5²= 25. 144+25= 169. It doesn't end there. Do the square root of 169 ---> √169=13.

Given that ABCD is a rectangle, if a diagonal line cuts from A to C make a two equal right angled triangles, the hypotenuse which is the length of AC is 13.

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c = √( a² + b² )

Given the data in the question;

Let line AC be the hypotenuse as it cuts the rectangle into two equal right angled triangle.

From Pythagorean theorem.

c = √( a² + b² )

AC = √( AB² + BC² )

AC = √( 12² + 5² )

AC = √( 144 + 15 )

AC = √169

AC = 13

Therefore, given that ABCD is a rectangle, if a diagonal line cuts from A to C make a two equal right angled triangles, the hypotenuse which is the length of AC is 13.

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Answer:

170

one-hundred seventy

Step-by-step explanation:

[tex]2(5(7+4(17 - 9)-22))=\\2(5(7+4(8)-22))=\\2(5(7+32-22))=\\2(5(39-22))=\\2(5(17))=\\2(85)=\\170[/tex]

Answer:

170.

Step-by-step explanation:

2{ 5[7 + 4(17 - 9) - 22]}

2{5[7+32 -22]}

2{5[17]}

2[85] = 170

Answer:

540 kilometers

Step-by-step explanation:

The car travels 45 kilometers every 1 hour.

In 12 hours, 45 × 12 = 540

The car will have covered a distance of 540 kilometers.

If car travels an average speed of 45km per hour, the car covers a distance of 540 kilometers in 12 hours.

To calculate the distance covered by the car in 12 hours, we can use the formula:

Distance = Speed × Time

Given that the average speed of the car is 45 km per hour and it travels for 12 hours, we can plug these values into the formula:

Distance = 45 km/h × 12 hours

Distance = 540 km

The formula for calculating distance is straightforward: it multiplies the speed (rate of motion) by the time taken. In this case, the car travels at a constant speed of 45 km/h, which means it covers 45 kilometers every hour.

By traveling for 12 hours, it accumulates a total distance of 540 kilometers. This calculation is useful for determining how far an object, in this case, a car, will travel given its speed and the duration of its journey.

To learn more about distance/speed click on,

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Answer:

The psychologist finds that the estimated Cohen's d is 0.583.

Step-by-step explanation:

The Cohen's d is used to calculate the effect size, appied when a null hypothesis is rejected.

It can be calculated for this case of population mean as:

[tex]d=\dfrac{M-\mu}{\sigma}=\dfrac{6.5-5.8}{1.2}=\dfrac{0.7}{1.2}=0.583[/tex]

The psychologist finds that the estimated Cohen's d is 0.583.

Answer:

First step

y = x + 5

Second step

x = y + 5

Next step

x - 5 = y

Last step

y = x - 5

Hope this helps you.

Answer:

V = 150 pi  units ^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

V = pi 10^2 * 15

V = 1500 pi  units ^3

Explanation: Notice that the figure shown here is a cylinder.

To find the volume of a cylinder, start with the formula

for the volume of a cylinder which is v = πr²h.

Here, notice that our cylinder has a radius of 10 and a height of 15.

So we have (π)(10)²(15).

Start by simplifying the exponent.

(10)² is (10)(10) or (100 units²).

So we have (π)(100 units²)(15).

Now, (100 units²)(15) is 1,500 units³.

So we have 1,500π units³.

So your answer is D.

Answer:

c. 0.10

Step-by-step explanation:

Hello!

To accept a batch of components, the proportion of defective components is at most 0.10.

X: Number of defective components in a sample of 10.

This variable has a binomial distribution with parameters n=10 and p= 0.10 (for this binomial experiment, the "success" is finding a defective component)

The distributor will accept the batch if at most two components are defective, symbolically:

P(X≤2)

Using the tables for the binomial distribution you can find the accumulated probability for a sample of n=10 with probability of success of p= 0.10 and number of successes x= 2

P(X≤2)= 0.9298

I hope this helps!

Answer:

Create a table of xy values or use a graphing calc.

Step-by-step explanation:

Answer:

Three points you can plot are: (-6, -3.5) (-7, -5) (0, 5.5).

Step-by-step explanation:

You can use a graphing calculator to determine the points. Attached is an image.

Hope this helps! :)

Answer:

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the population proportion significantly differs from 0.89.

The requirements for the test are satisfief.

n(1-p)=70>10

Step-by-step explanation:

This is a hypothesis test for a proportion.

There are 3 requirements to have a valid test of proportion: random sample, independence and normal.

For the first two (random and independent sample) we don't have details, but we assume the sampling has been random.

The latter can be verified by calculating np and n(1-p):

[tex]np=430>10\\\\n(1-p)=70>10[/tex]

Both are bigger than 10, so the normal approximation can be considered appropiate.

The claim is that the population proportion significantly differs from 0.89.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.89\\\\H_a:\pi\neq 0.89[/tex]

The significance level is 0.01.

The sample has a size n=500.

The sample proportion is p=0.86.

[tex]p=X/n=430/500=0.86[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.89*0.11}{500}}\\\\\\ \sigma_p=\sqrt{0.000196}=0.014[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.86-0.89+0.5/500}{0.014}=\dfrac{-0.029}{0.014}=-2.072[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=2\cdot P(z<-2.072)=0.038[/tex]

As the P-value (0.038) is greater than the significance level (0.01), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the population proportion significantly differs from 0.89.

Answer:

Solution,

Principal( P)= £ 2000

Rate (R)= 1.5%= 1.5/100

Time (t)= 6 years

Interest=?

Now,

[tex]interest = principal \times rate \times time \\ \: \: \: \: = 2000 \times \frac{1.5}{100} \times 6 \\ \: \: = 180[/tex]

Therefore, he will earn £ 180 in 6 years.

Hope this helps..

Good luck on your assignment..

Answer:

5

Step-by-step explanation:

h(2)=5(2)-5

5 x 2 = 10

10 - 5 = 5

The value of the function h(x) = 5x - 5 at x = 2 will be 5.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

The function is given below.

h(x) = 5x - 5

Then the value of the function at x = 2 will be

h(2) = 5 (2) - 5

h(2) = 10 - 5

h(2) = 5

The value of the function h(x) = 5x - 5 at x = 2 will be 5.

More about the value of expression link is given below.

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Answer:

6

Step-by-step explanation:

you have to distributw the 4 to the 1/4 so essentially youre multiplying the exponents. think of it as 4*1/4 and youll have 4/4 which equals to 1. 6^1 is just 6 so thats the answer

well first you have to multiply 6 by 1/4 and then you have to do this: 1.5*1.5*1.5*1.5 to get your answer i think....

Answer:

Step-by-step explanation:

To get the missing values in the table, we will factorize the given expression and compare the factored expression with the expression containing the missing constants.

1) For the expression x²+2x-8, on factorizing we have;

x²+2x-8

= (x²+4x)-(2x-8)

Factoring out the common terms from both parenthesis;

= x(x+4)-2(x+4)

= (1x+4)(1x-2)

=  (1x-2)(1x+4)

Comparing the resulting expression with (ax+b)(cx+d)

a = 1, b = -2, c = 1 and d = 4

2) For the expression 2x³+2x²-24x

Factoring out the common term we will have;

= 2x(x²+x-12)

= 2x(x²-3x+4x-12)

= 2x{x(x-3)+4(x-3)}

= 2x{(x+4)(x-3)}

=  2x(1x-3)(1x+4)

Comparing the resulting expression with 2x(ax+b)(cx+d)

a = 1, b = -3. c = 1 and d = 4

3) For the expression 6x²-15x-9 we will have;

On simplifying,

= 6x²+3x-18x-9

= 3x(2x+1)-9(2x+1)

= (3x-9)(2x+1)

Comparing the resulting expression with (ax+b)(cx+d)

a = 3, b = -9, c = 2 and d = 1

Answer:

see picture attachment

Step-by-step explanation:

Answer:

  62°

Step-by-step explanation:

∠BOA is the supplement to the angle marked 56°, so is 124°. ∠BCA is an inscribed angle subtending the same arc (AB), so has half the measure of the arc.

m∠BCA = (1/2)(124°)

m∠BCA = 62°

Answer:

133

Step-by-step explanation:

1000 = 2 * 2 * 2 * 5 * 5 * 5

To not have a multiple of 10, you cannot have 2 and 5 as factors of the same number.

One number is 2^3 = 8.

The other number is 5^3 = 125.

8 * 125 = 1000, so the two do multiply to 1000.

Neither 8 nor 125 is a multiple of 10.

8 + 125 = 133

Answer:

133

Step-by-step explanation:

We are given that the product of two numbers is 1000. Let's first list out the factors of 1000 (factors are numbers that evenly divide into 1000):

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000

We see that the pairs are:

(1, 1000)

(2, 500)

(4, 250)

(5, 200)

(8, 125)

(10, 100)

(20, 50)

(25, 40)

An easy way to see if a number is divisible by 1000 is to check is it has a zero at the end. Notice that all of the pairs have at least one number that ends with at least 1 zero except (8, 125), so this is the pair of numbers we're looking for.

The sum is thus 8 + 125 = 133.

~ an aesthetics lover

Answer:

[tex]\frac{7\sqrt{x} }{x}[/tex]

Step-by-step explanation:

To simplify 7/√x, we need to rationalize:

[tex]\frac{7}{\sqrt{x} } (\frac{\sqrt{x} }{\sqrt{x} } )[/tex]

When we multiply the 2, we should get our answer:

[tex]\frac{7\sqrt{x} }{x}[/tex]

Answer:

[tex]\frac{7\sqrt{x} }{x}[/tex]

Step-by-step explanation:

[tex]\frac{7}{\sqrt{x} } \\\\\frac{7}{\sqrt{x} } * \frac{\sqrt{x} }{\sqrt{x} } \\\\\frac{7\sqrt{x} }{\sqrt{x\sqrt{x} } } \\[/tex]

[tex]\frac{7\sqrt{x} }{x}[/tex]

Hope this helps! :)

Answer:

¿Consideras que la gente que discrimina por aspectos como el color de la piel, clase social, por el género, etc., no saben lo que las personas valen y por eso no las valoran?

Answer:

14 units

Step-by-step explanation:

If l and m are two parallel lines and a point X is reflected across line l followed by a reflection across line m, then the distance between

X and X′ is 2d, where d is the distance between l and m. Since d = 7, the distance between B and B′′ is 2(7) = 14 units.

Answer:

(a) The odds for and against E are (8:1) and (1:8) respectively.

(b) The odds for and against E are (7:2) and (2:7) respectively.

(c) The odds for and against E are (59:41) and (41:59) respectively.

(d) The odds for and against E are (71:29) and (29:71) respectively.

Step-by-step explanation:

The formula for the odds for an events E and against and event E are:

[tex]\text{Odds For}=\frac{P(E)}{1-P(E)}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}[/tex]

(a)

The probability of the event E is:

[tex]P(E)=\frac{8}{9}[/tex]

Compute the odds for and against E as follows:

[tex]\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{8/9}{1-(8/9)}=\frac{8/9}{1/9}=\frac{8}{1}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-(8/9)}{8/9}=\frac{1/9}{8/9}=\frac{1}{8}[/tex]

Thus, the odds for and against E are (8:1) and (1:8) respectively.

(b)

The probability of the event E is:

[tex]P(E)=\frac{7}{9}[/tex]

Compute the odds for and against E as follows:

[tex]\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{7/9}{1-(7/9)}=\frac{7/9}{2/9}=\frac{7}{2}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-(7/9)}{7/9}=\frac{2/9}{7/9}=\frac{2}{7}[/tex]

Thus, the odds for and against E are (7:2) and (2:7) respectively.

(c)

The probability of the event E is:

[tex]P(E)=0.59[/tex]

Compute the odds for and against E as follows:

[tex]\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{0.59}{1-0.59}=\frac{0.59}{0.41}=\frac{59}{41}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-0.59}{0.59}=\frac{0.41}{0.59}=\frac{41}{59}[/tex]

Thus, the odds for and against E are (59:41) and (41:59) respectively.

(d)

The probability of the event E is:

[tex]P(E)=0.71[/tex]

Compute the odds for and against E as follows:

[tex]\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{0.71}{1-0.71}=\frac{0.71}{0.29}=\frac{71}{29}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-0.71}{0.71}=\frac{0.29}{0.71}=\frac{29}{71}[/tex]

Thus, the odds for and against E are (71:29) and (29:71) respectively.

Answer:

Theoretical probability = 50%

Experimental probability varies.

See below for explanation.

Step-by-step explanation:

This is a problem on theoretical and experimental probability. The results obtained would enable you understand their differences.

The theoretical probability is the result that is expected to happen, but it isn't always what eventually happens.

The theoretical probability of a coin landing on heads is ½ or 50%. This is same for tails.

The experimental probability is the probability obtained from carrying out the experiment. As this is the result of what actually happens, the experimental probability could be lesser  or greater than or equal to 50%.

You are required to carry out the experiment. This is because the result would vary from person to person as well as from one experiment to the other.

First, make a table for the number of trials, outcome (head and tail each) and the frequency. Pen down the result for each of the experiment carried out. You can use a tally to make it easy for compilation.

See attachment for table.

Theoretical probability of 10 trials:

Head= 5, tail = 5

Theoretical probability of 30 trials:

Head= 15, tail = 15

Theoretical probability of 100 trials:

Head= 50, tail = 50

It all amount to 50% each

So do your experiment and record the results. Afterwards compare your result  which is the experimental probability

for head and tail with the theoretical theoretical.

Also compare your result with that of your classmate.

Answer:

When f(x) = 2, x = 1/2, -2/3

Step-by-step explanation:

Step 1: Set equation equal to 2

[tex]2 = \frac{x-2}{3x^2 +x -2}[/tex]

Step 2: Multiply both sides by denominator

2(3x² + x - 2) = x - 2

Step 3: Distribute

6x² + 2x - 4 = x - 2

Step 4: Isolate everything to one side

6x² + x - 2 = 0

Step 5: Factor

(2x - 1)(3x + 2) = 0

Step 6: Find roots

x = 1/2, -2/3

Answer:

B

Step-by-step explanation:

X^2  3*3=9

X^2 2*2=4

Hope this helps. I've done something like this before. (: Good luck

Answer:

B: x^2-9/x^2-4

Step-by-step explanation:

numerator:

(x+3)(x-3) = x^2-3x+3x-9 = x^2 - 9

denominator:

(x+2)(x-2) = x^2-2x+2x-4 = x^2 - 4

final answer:

x^2-9 /x^2-4