Question

Solve for x : 1/x-3 - 1/x+5 =1/6
where x≠3, 5​

Answer 1

$\frac{1}{x - 3} - \frac{1}{x + 5} = \frac{1}{6} \\ \frac{(x + 5) - (x - 3)}{(x - 3)(x + 5)} = \frac{1}{6} \\ \frac{x + 5 - x + 3}{ {x}^{2} + 5x- 3x - 15} = \frac{1}{6} \\ \frac{8}{ {x}^{2} + 2x - 15} = \frac{1}{6} \\{x}^{2} + 2x - 15 = 48 \\ {x}^{2} + 2x - 63 = 0 \\ {x}^{2} + 9x - 7x - 63 = 0 \\ x(x + 9) - 7(x + 9) = 0 \\ (x + 9)(x - 7) = 0$

Therefore, x = -9 or x = +7