Question

Solve `(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2 1/2`

Answer 1

`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2 1/2`

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

`=> (x^2 - 6x + 9 + x^2 + 6x + 9)/(x^2 - 9) = 5/2`

`=> 2(2x^2 + 18) =  5(x^2 - 9)`

`=> 4x^2 + 36 = 5x^2 - 45``

`=> x^2 - 81 = 0`

`=> x^2 - 9^2 = 0`

=> (x + 9)(x - 9) = 0

if x + 9 = 0  or x - 9 = 0

then x = -9 or x  = 9