Question

x+5/x-5 - x-5/x+5 = 15/4​

Answer 1

Answer:

NO solution

$\Huge \boxed{X=0}$

Step-by-step explanation:

To solve this problem, first you have to isolate by the x from one side of the equation.

First, least common multiple of x is 4x.

x*4x+5/x*4x-5*4x-x*4x-5/x*4x+5*4x=15/4*4x

Solve.

0=15x

Next, switch sides.

15x=0

Then, divide by 15 from both sides.

15x/15=0/15

Solve.

0/15=0

Therefore, there are NO solutions and x=0, which is our answer.

Hope this helps!

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Answer 2

x+5/x-5 - x-5/x+5 = 15/4

{(x+5)^2 - (x -5)^2}/x^2 -25 = 15/4

(x+5+x-5)(x+5-x +5) /(x-5)(x+5)=15/4

20x/(x^2 -25)=15/4

15x^2 - 375 -80x= 0

3x^2 - 75 - 16x =0

9x^2 - 48x + 8^2 - 139=0

(3x - 8)^2 -( sqrt139)^2=0

(3x - 8 + sqrt139)(3x -( 8 +sqrt139))=0

x = (8 - sqrt139)/3

and (8+sqrt139)/3