Mathematics College


[tex]\frac{1}{x {}^{2} - 3 } = \frac{ \sqrt{3} }{x + \sqrt{3} } - \frac{2}{ \sqrt{3} - x } [/tex]
can someone please solve this?
​

Answers

Answer 1

Answer:

[tex]\boxed{\textsf{ The value of x is \textbf{ 8 + 6}$\sqrt{3 }$.}}[/tex]

Step-by-step explanation:

Here we are given a equation which we need today simplify and solve for x .The given equation to us is :-

[tex]\sf\implies \dfrac{1}{x {}^{2} - 3 } = \dfrac{ \sqrt{3} }{x + \sqrt{3} } - \dfrac{2}{ \sqrt{3} - x } [/tex]

Let's simplify the equation :-

[tex]\sf\implies \dfrac{1}{x {}^{2} - 3 } = \dfrac{ \sqrt{3} }{x + \sqrt{3} } - \dfrac{2}{ \sqrt{3} - x } \\\\\sf\implies \dfrac{1}{x^2-3}=\dfrac{\sqrt3}{x+\sqrt3}-\dfrac{2}{-(x-\sqrt3)}\\\\\sf\implies \dfrac{1}{x^2-3}=\dfrac{\sqrt3}{x+\sqrt3}+\dfrac{2}{x-\sqrt3}\\\\\sf\implies \dfrac{1}{x^2-3}=\dfrac{\sqrt3(x-\sqrt3)+2(x+\sqrt3)}{(x+\sqrt3)(x-\sqrt3)}\\\\\sf\implies \dfrac{1}{x^2-3}=\dfrac{\sqrt3x-3+2x+2\sqrt3}{x^2-3}\\\\\sf\implies 1=\sqrt3x-3+2x+2\sqrt3 \\\\\sf\implies \sqrt3x+2x = 4-2\sqrt3\\\\\sf\implies x(\sqrt3 +2)=4-2\sqrt3\\\\\sf\implies x =\dfrac{4-2\sqrt3}{\sqrt3+2}\\\\\sf\implies x =\dfrac{ (4-2\sqrt3)(\sqrt3-2)}{(\sqrt3+2)(\sqrt3-2)}\\\\\sf\implies x =\dfrac{-8-6\sqrt{3}}{3-4}\\\\\sf\implies \boxed{\pink{\sf x =8+6\sqrt3}}[/tex]

[tex]\frac{1}{x {}^{2} - 3 } = \frac{ \sqrt{3} }{x + \sqrt{3} } - \frac{2}{ \sqrt{3} - X } [/tex]can

Related Questions

PLEASE HELP SOLVE THIS WUESTION SOLVE FOR y

Answers

Answer:

y = 5

Step-by-step explanation:

12^2 + y = 13^ 2

144 + y = 169

169 - 144 = 25

sqrt of 25 = 5

y = 5

Answer:

A, y=5

Step-by-step explanation:

I just did it right now

describe a family member in 3-5 sentences (use nouns) make it easy and simple please!!

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Ok! ———- is ———- because of ————. They have ———- hair color and ———— eye color. I think they are ———— because of ————. They like to —————- because —————.

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Answers

Answer: where is the line segment

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

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Answers

Answer:

the sine Is 5/13

Step-by-step explanation:

use the trigonometric identity : sin^2+ cos^2 = 1

so the sine Is sqrt(1-(12/13)^2) = 5/13

sqrt means Square root btw

What is 3/5 divided by 3/4

Answers

3/5 *4/3

1/5*4/1=4/5

=.8

hope it helps

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That can be simplified to 4/5

Write a word description of the set.
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Answers

this set of numbers counting by ones or the addition of one each time
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Given that IG FT which of the following statements is true

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Answer:

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Step-by-step explanation:

Find the coordinates of the point that is located 8 units below the x-axis and 3 units to the left of the y-axis

Answers

-8,-3 if i read that correctly, that should be the answer.

18% of the the students at a school are in year 8 and 16% of the students are in year 9. If the school has 126 tera 8 students, determine the number of year 9 students.​

Answers

Answer:

112

Step-by-step explanation:

The general form of all percentage questions is: the chunk= (some percentage) (of the whole), or c=p*w

We know that 18% of students are 8th grade and that is 126 students, so p = 0.18 and c=126 (126 students are 18% of the whole school)

126 = (0.18)w, divide both sides by 0.18

126/(0.18) = w = 700

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c = (0.16) 700 = 112 students

ice cream is served for dessert if Gio serves himself and 3 friends half a cup of ice cream how many total pints did Gio and his friends eat?

Answers

Answer:

0.25 pints

Step-by-step explanation:

To find how many pints they ate, find the number of pints in half a cup.

In 1 cup, there are 0.5 pints.

This means in half a cup, there will be 0.25 pints.

So, Gio and his friends ate 0.25 pints

9(2+2p) show distributive property
​

Answers

Answer:

9(2+2p)

9 x2 + 9 x 2p

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A carpet salesman sold 5,000 yards of carpet in one month at an average of $3 per yard. His commission was 16%. How much money did he make that month?

Answers

Answer:

5000x3.00= total sales  15000 x 16% or.16

= 2400

Step-by-step explanation:

1.Find Gross Sales

2. Get retail sales  3.00 x 5000

3. Total Sales times commission  15000 x .16

Kristin wants to buy a pair of jeans that cost $35 and are on sale
20% off. She is also buying two T-shirts at a full price of $9.99 each.
She must pay 6.5% sales tax. How much will she pay for the clothes

Answers

Answer:

$51.10

Step-by-step explanation:

First, find 20% of $35, then add the sale price of the jeans and the two t-shirts. Take the total and find the sales tax and add that onto the cost.

100 - 20 = 80 If you multiply the jeans by 80% it gives you the price for the jeans saving you from having to subtract the discount from the original price.

35 * 0.80 =  $28.00 jeans                     28.00                             47.98

                                                                  9.99                             + 3.12

                                                             +   9.99                            $51.10

                                                                47.98

                                                           X   0.065

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lol,j,bhkgkjhkhkhkhukgiuguk

Answers

Answer:

wioajfcskaljfcksjhnfkmdesdn,k  obviously

Step-by-step explanation:

What is the ratio in which the point P(3/4,5/12) decides the line segment joining points A(1/2,3/2) and B(2,-5)

​

Answers

Given:

The point [tex]P\left(\dfrac{3}{4},\dfrac{5}{12}\right)[/tex] divides the line segment joining points [tex]A\left(\dfrac{1}{2},\dfrac{3}{2}\right)[/tex] and [tex]B(2,-5)[/tex].

To find:

The ratio in which he point P divides the segment AB.

Solution:

Section formula: If a point divides a segment in m:n, then the coordinates of that point are,

[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]

Let point P divides the segment AB in m:n. Then by using the section formula, we get

[tex]\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{m(2)+n(\dfrac{1}{2})}{m+n},\dfrac{m(-5)+n(\dfrac{3}{2})}{m+n}\right)[/tex]

[tex]\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{2m+\dfrac{n}{2}}{m+n},\dfrac{-5m+\dfrac{3n}{2}}{m+n}\right)[/tex]

On comparing both sides, we get

[tex]\dfrac{3}{4}=\dfrac{2m+\dfrac{n}{2}}{m+n}[/tex]

[tex]\dfrac{3}{4}(m+n)=\dfrac{4m+n}{2}[/tex]

Multiply both sides by 4.

[tex]3(m+n)=2(4m+n)[/tex]

[tex]3m+3n=8m+2n[/tex]

[tex]3n-2n=8m-3m[/tex]

[tex]n=5m[/tex]

It can be written as

[tex]\dfrac{1}{5}=\dfrac{m}{n}[/tex]

[tex]1:5=m:n[/tex]

Therefore, the point P divides the line segment AB in 1:5.

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Answers

Answer:

The inequality that will be used would be

x + 22 <= 55

When plotting points on the coordinate plane below, which point would lie on the x-axis?



(6, 0)
(0, 2)
(3, 8)
(5, 5)

Answers

Answer: (6,0)

Coordinate points are always written in pairs of the x- and y-coordinate: (x, y). Knowing this, the point would need to have a y-value of 0 in order to lie on the x-axis (otherwise, it would be on a random spot on the grid). The only coordinate point with a y-value of 0 is (6, 0). Therefore, the coordinate point (6, 0) lies on the x-axis.

Please refer to the attached graph below to see all the coordinate points.

estimate the product of 26.4×2.7​

Answers

Answer:..

Step-by-step explanation:

Answer:

Step-by-step explanation:

okay, 26.4*2.7 = 26*3 (when estimated)

26*3=78(or just somewhere around 70)

Find the measure of the indicated angel.

A) 30 degrees
B) 35 degrees
C) 25 degrees
D) 40 degrees

Answers

Answer:

D

Step-by-step explanation:

44+32=76

180-76=104

104+36=140

180-140=40

D)40

Two weeks ago price was $220 now it's $325. What is the percent increase? What is percent increase if there is an additional $50 baggage fee with the new ticket price?

Answers

Answer:

68.18%

Step-by-step explanation:

325+50=375

375-220=155

155÷220×100%

≈68.18%

Hello pls help me with two of these questions;)

Answers

Answer:

1-A-15

2-C

Step-by-step explanation:

7-21 is an increase by 3 times, so 5*3=15

The second is kinda blurry, so it's a little hard to explain.

Decrease 60 by 0.75 of itself ​

Answers

Answer:

15

Step-by-step explanation:

(0.75 of 60)  

0.75 * 60 = 45

(decrease 60 by answer)

60 - 45 = 15

yes, 15
60 x .75 =45
60-45 =15

If a square has a side of (3x+5), what is its perimeter?”
O
a.6x + 10
b.3x + 15
c.123 + 5
d.123 + 20

Answers

Answer:

Step-by-step explanation:

The perimeter of a square is four times a side. We are told a side equals 3x+5 so

P=4S

P=4(3x+5)

P=12x+20

m∠FDC=124°; m∠EAB=2x, m∠ACG=4x. Find: x, m∠ACD

Answers

Answer:

x=28 degrees

Step-by-step explanation:

4x = 28*4 = 112

180 degrees - 112 = 68

ACD = 68

Determine the center of the circle whose equation is (x – 5)2 + (y + 7) = 14

Answers

Answer:58 approximately c

Step-by-step explanation:

Jimmy estimates that a pitcher holds 4.5 liters of liquid. It actually holds 4.8 liters. What is the percent error between his estimate and the actual volume of the pitcher?
A. 1/3%
B. 1 1/3%
C. 6 1/4%
D. 6 2/3%

Answers

Answer:

the answer is 6 1/4%. I hope it helps!

In 1989 the population of Arizona was 3,622,184. In 1999 the population was 4,778,332. What is the percent of change from 1989 to 1999?

Answers

Answer- 31.9%

3,622,184 =100%
4,778,332= x
Criss cross
477,833,200= 3,622,184x
Divide to get x alone
X= 131.9
131.9 - 100= 31.9%
Because it asks for the change

The angles of a triangle add up to 180 degrees.

The second angle is 20 degrees larger than the smallest angle.

The third angle is 3 times as big as the smallest angle.

Find the measure of the smallest angle (in degrees)

Answers

Answer: 32 degrees

Step-by-step explanation:

small angle : x

middle angle: x + 20

large angle: 3x

Form an equation: 5x + 20 = 180

5x = 180 - 20

5x = 160

x = 160/5

x = 32

Simplify the fractions using the greatest common factor and division 4/8 =

Answers

Answer:

2/4

Step-by-step explanation:

PLEASEEEE HELPPP
Ben Frank is an electrician who installs lighting fixtures. He charges (in dollars) his clients 15h +40f
where h is the number of hours worked and f is the number of fixtures installed.
How much does Ben Frank charge when he works 7 hours and installs 9 fixtures?

Answers

Answer:

465 Dollars

Step-by-step explanation:

15h+40f = Amount Charged

if: h = 7

   f = 9

15(7)+40(9) = Amount Charged

105 + 360 = Amount Charged

465 = Amount Charged

He will charge 465 dollars.

Answer:$465Steps and explanation of why:

Ben works 7 hours installing 9 fixtures. This tells us that h = 7, and f = 9. So, let's substitute h = 7 and f = 9 into the expression and evaluate:

Step 1:

15h + 40f

Step 2:

= 15(7) + 40(9)

Step 3:

= 105 + 360

Step 4:

= $465

Hope this helps!! Remember to get good grades, and to stay safe :))

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