Question

`(3)/(x+3) -(4)/(x-3)=(5x)/(x^(2) -9)`

Answer 1

Explanation:

`(3)/(x+3)-(4)/(x-3)=(3*(x-3))/((x+3)(x-3))-(4(x+3))/((x-3)(x+3))\\\\=(3*x-3*3)/((x+3)(x-3))-(4*x+4*3)/((x+3)(x-3))\\\\=(3x-9)/(x^(2)-3^(2))-(4x+12)/(x^(2)-3^(2))\\\\=(3x - 9 -(4x + 12))/(x^(2)-3^(2))\\\\=(3x-9-4x-12)/(x^(2)-9)\\\\=(-x-21)/(x^(2)-9)\\\\`

`(3)/(x+3)-(4)/(x-3)=(5x)/(x^(2)-9)\\\\(-x-21)/(x^(2)-9)=(5x)/(x^(2)-9)\\\\-x-21=(5x)/((x^(2)-9))*(x^(2)-9)\\`

-x - 21 = 5x

Add 'x' to both sides

-x -21 +x = 5x + x

-21 = 6x

6x = -21

x = -21/6

= -7/2

x = -3.5