Question

Solve the following quadratic equations by factorization:

`(x - 3)/(x + 3) - (x + 3)/(x - 3) = 48/7; x ≠ 3, -3`

Answer 1

We have been given

`(x-3)/(x+3)-(x+3)/(x-3)=48/7`

7(x² + 9 - 6x - x² - 9 - 6x) = 48(x² - 9)

48x² + 84x - 432 = 0

4x² + 7x - 36 = 0

Therefore,

4x² + 16x - 9x - 36 = 0

4x(x + 4) - 9(x + 4) = 0

(4x - 9)(x + 4) = 0

Therefore,

4x - 9 = 0

4x = 9

x = `9/4`

or,

x + 4 = 0

x = -4

Hence, x = `9/4` or x = -4.