find all the possible of x for which of the below is true:

[tex] \frac{2x}{x + 3} + \frac{3}{x - 3} = \frac{8}{x^{2} - 9 } [/tex]

Answers

Answer 1

Answer:

x = [tex]\frac{1}{2}[/tex] , x = 1

Step-by-step explanation:

Given

[tex]\frac{2x}{x+3}[/tex] + [tex]\frac{3}{x-3}[/tex] = [tex]\frac{8}{x^2-9}[/tex] ← denominator is a difference of squares

[tex]\frac{2x}{x+3}[/tex] + [tex]\frac{3}{x-3}[/tex] = [tex]\frac{8}{(x+3)(x-3)}[/tex]

Multiply through by (x + 3)(x - 3) to clear the fractions

2x(x - 3) + 3(x + 3) = 8 ← distribute left side and simplify

2x² - 6x + 3x + 9 = 8

2x² - 3x + 9 = 8 ( subtract 8 from both sides )

2x² - 3x + 1 = 0 ← in standard form

(2x - 1)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

x - 1 = 0 ⇒ x = 1


Related Questions

JELLO HELLO KNOCKS FOR HELP

Answers

Wait imma try to solve this

Answer:

I think it's 9×30=270 (given

270-180 (sum of triangle

=90°

What is the length of the hypotenuse?

Answers

Answer:

65 cm

Step-by-step explanation:

16^2 x 63^2 = 65^2

Need help with this question!!

Answers

x^2 = 2 × ( 2 + 4 )

x^2 = 2 × 6

x^2 = 12

x = √12

x = √4 × 3

x = 2√3

Answer:

x = 4

Step-by-step explanation:

Assume the dimension 4 is a diameter, and x is a tangent to the circle.

Use the tangent/secant formula to find

x*x = 2*(2+4)

x^2 = 16

x = 4

74,308 Problem: Round the number above to the nearest ten.

Answers

Answer:

74,310

Hope this helped! ^^

Answer:

[tex] = 74,310[/tex]

step by step explanation:

PLEASE HELP DUE IN 5 MINUTES!! NO LINKS! HELP PLEASE!!

Answers

Answer:

Step-by-step explanation:

its about 263.08!

Answer: about 263.08 sq meters (choice C)

====================================================

Explanation:

We'll use this formula

S = (x/360)*A

where,

S = area of pie slice, aka sectorx = central angle in degreesA = area of full circle

We'll plug in S = 85.5 and x = 117 to find solve for A.

S = (x/360)*A

85.5 = (117/360)*A

85.5*(360/117) = A

A = 85.5*(360/117)

A = 263.076923076923 which is approximate

A = 263.08 square meters (choice C)

------------

Side note: As the formula suggests, the x/360 portion is the fractional portion of the full area A. For example, if x = 180 degrees, then x/360 = 180/360 = 1/2, meaning we'll take half of the full circle area to get S.

The amount of rona cases in Gotham city is 540 people for the first ½ of 2020. In July, a rona spike at the rate of 5.2 people for each day in the month hits. Additionally, the joker has infected all of Arkham Asylum’s 225 patients with the virus. What month will you hit 1,000 cases of rona in Gotham?

Answers

Answer:

Imma but it in the comments because i can't put it on here plus i can't put the thing on here either that's why i didn't do it yesterday

Step-by-step explanation:

The number of patients treated at Dr. Frank's dentist office each day was recorded for nine days: 18,
19, 19, 4, 14, 8, 22, 3, 1. Using the given data, find the mean for this sample.

A. 12

B.19

C. 29

D. 14

Answers

Answer: 12

Step-by-step explanation: The mean is basically the average. So, start by lining up the numbers from smallest to largest. 1, 3, 4, 8, 14, 18, 19, 19, 22. Then, add them all together. You get 108. Then, divide 108 by the number or numbers in the data set, which in this case is 9. So 108 divided by 9 = 12. Your answer is A. --> 12

Hope that helped!!

Find the value of x and y.

Answers

Answer:

x=34[tex]\sqrt{2}[/tex]

y=34[tex]\sqrt{3}[/tex]

Step-by-step explanation:

NEED HELP HERE PLEASE!! π∆π

Give the value of the six trigonometric ratios in the figure.​

Answers

Answer:

Step-by-step explanation:

take theta as reference angle

using sin rule

sin theta=opposite/hypotenuse

sin theta=3/5

sin theta=0.60

theta=sin 37 degree

therefore the value of theta is 37 degree.

PLEASE I NEED HELP I DONT UNDERSTAND HOW TO DO ILL GIVW MORE IF RIGHT

Answers

Answer:

the second one

Step-by-step explanation:

PLEASE HELP WILL GIVE BRAINLIST​

Answers

Answer:

B

Step-by-step explanation:

∠ 3 and ∠ 8 are alternate angles and are congruent, then

6x + 3 = 4x + 29 ( subtract 4x from both sides )

2x + 3 = 29 ( subtract 3 from both sides )

2x = 26 ( divide both sides by 2 )

x = 13 → B

30 POINTS I WILL GIVE U BRAINLIEST AND THANKS AND 5 STARS please help this is very important this is a big part of my grade

Answers

Answer:

[tex]1.\:2^x=64, x=\boxed{6},\\2.\:x=\left(\frac{2}{3}\right)^3,x=\boxed{\frac{8}{125}}\\3.\:3\cdot (3^4)=3^x, x=\boxed{5}\\4.\:\frac{16}{25}=x^2,x=\boxed{\frac{4}{5}},[/tex]

Step-by-step explanation:

[tex]1.\\\\2^x=64,\\\log 2^x=\log64,\\x\log 2=\log 64,\\x=\frac{\log 64}{\log 2}=\boxed{6}[/tex]

[tex]2.\\x=\left(\frac{2}{5}\right)^3=\frac{2^3}{5^3}=\boxed{\frac{8}{125}}[/tex]

3. This problem incorporates an exponent property.

Exponent property used: [tex]a^b\cdot a^c=a^{(b+c)}[/tex], yielding an answer of [tex]\boxed{5}[/tex]

[tex]4.\\\\\frac{16}{25}=x^2,\\x=\sqrt{\frac{16}{25}}=\frac{\sqrt{16}}{\sqrt{25}}=\boxed{\frac{4}{5}}[/tex]

Answer:

1. 6

2. 8/25

3. 5

4. 4/5

Step-by-step explanation:

The following pie chart represent the number of valid votes by four students the total no of voters is 720. A) who has won and by how many votes B) who got the minimum c) how man votes are obtained
Plz hurry plz I need urgently

Answers

Answer:

I only know this much.....

A) Deepthi has won the election.

B) Rashmi got minimum number of votes.

Jensen goes to the store with $4. He buys 3 pencils for $0.70 each and
some erasers. Each eraser costs $0.50. Enter the maximum number of
erasers he can buy.

Answers

Answer:

3 erasers.

Step-by-step explanation:

Let p = pencils and e = erasers. Since we know that Jensen has $4, we can set up the following inequality and solve for e.

0.70p + 0.50e ≤ 4

0.70(3) + 0.50e ≤ 4

2.10 + 0.50e ≤ 4

0.50e ≤ 1.90

e ≤ 3.8

Since erasers are usually bought as whole items, the maximum amount of erasers Jensen can buy is 3.

the radius of a circle is 14.2 m. Find the circumference to the nearest tenth.​

Answers

Answer:

C=89.2

Step-by-step explanation:

The formula of the circumference of a circle is C=2piR (or C=piD). Now, when calculating, plug in the numbers, giving you C=2pi14.2. Multiply everything, you get a super long irrational number; just round. You will get 89.2.

Which is not a solution of 5g - 6 => 24?
A. g=6
B. g=10
C. g. 20
D. g=-8

Answers

Answer:

A. g=6

Step-by-step explanation:

5g-6=24

5g=30

g=30/5

g=6

Answer:

D, g = -8

Step-by-step explanation:

5 (-8) - 6 => 24

-40 - 6 => 24

-46 is NOT greater than or equal to 24.

What is the volume of the following rectangular prism?
8/3units
21/2units2
Volume =___ units3​

Answers

Answer:

73.5

Step-by-step explanation:

Step 1: 21/2 divided by 2 = 21/4

Step 2: 21/4 times 21/4 times 8/3 =

Answer: 73.5

The green shaded box is there to show that that is the base are to find the two sides that were multiplied to get that do the first step. Then do your basic volume formula: length times width times height.

please help me!

a) 280in2
b) 300in2
c) 150in2
d) 100in2

Answers

Answer:

C) 150

Step-by-step explanation:

a recipe for pancakes requires 1 3/4 cups of milk. how much milk is needed to get twice as many pancakes

Answers

Answer:

7/2 cups of milk.

Step-by-step explanation:

1 3/4=7/4

2(7/4)=14/4=7/2

Answer:

7/2 cups of milk.

Step-by-step explanation:

If you want double the pancakes You must double the amount of milk:

First change it into an improper fraction:

1 3/4=7/4

then multiply it by two and simplify:

2(7/4)=14/4=7/2

What is that number in scientific notation form??

Answers

Answer:

D. 3.7 × 10⁶

Step-by-step explanation:

3.7 × 10⁶

3700000

Help me with this please

Answers

Answer:

F'

Your answer is correct

Step-by-step explanation:

The image most of the time we will put ' prime on it to let the other know that this is the image

What is the range of the function graphed below?

Answers

Answer:

C.

[tex] - \infty < y < \infty [/tex]


Imani is a scientist working with a cylindrical beaker. The base of the right cylinder has a diameter of 19 cm. She fills the
beaker with 2256.254 Cms of an acid. Approximately how high did the acid fill up the beaker?

Answers

Answer:

7.96 cm

Step-by-step explanation:

radius of bottom: 19/2 = 9.5

area of bottom = pi * r^2 = 283.53

height * base area = volume

Look at the picture

Answers

Its d because 16/12=1.33 same with 20/15 and 40/30 so its 24x1.33 which is 32 there for d is correct

4x+2=-13 solve for x

Answers

Answer:

Solution given

4x+2=-13

subtract each term by 2

4x+2-2=-13-2

divide both side by 4

4x/4=-15/4

we get

x=-15/4

is a required answer.

Let's solve:

[tex]4x+2=−13[/tex]

Step 1: Subtract 2 from both sides.

[tex]4x+2−2=−13−2 \\ 4x = - 15[/tex]

Step 2: Divide both sides by 4.

[tex] \frac{4x}{4} = \frac{ - 15}{4} [/tex]

Answer:

[tex] \frac{ - 15}{4} [/tex]

Jina has scored 79, 85, 89 and 68 on her previous four tests. What score does she need on her next test so that her mean is 80?

Answers

Answer:

79

Step-by-step explanation:

79, 85, 89, 68 have a mean of 80.25 according to calculator.net. the number itself Is close to the number you want, in this case 80, i input 80, but it gave me a score of 80.2, so i tried again with 81, it gave me a score of 80.4, so the third attempt was successful with 79 being the input and 80 the output

calculator.net is approved on my school computer so there is a chance it is on yours as well.

Find the HCF of 12 and 16 ​

Answers

Answer:

4  Hope that helped

The answer is four please tell me if this helped

(5. solve for x )
2/5 + x = 1

Answers

X=3/5 for exact form of decimal it is x=0.6

please help :),))))

Answers

Answer:

option 1

Step-by-step explanation:

The rate of increasing is the fastest in exponential functions.

Then comes powers and last logarithmic functions.

The order it increases at the fastest rate.

[tex]log < powers < exponential[/tex]

I need help with this one thank you.

Mike owes his brother $9.55. He borrows $10.75 more from his brother. Which of the following best represents Mike's debt to his brother?

A B C D +$20.20 -$20.30 -$1.20 +$18.80​

Answers

Answer:

C - $20.30

Step-by-step explanation:

-9.55 + (-10.75) = - 20.3

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