Question

Solve:

`1/(18 - x) - 1/(18 + x) = 1/24` and x > 0

Answer 1

Given quadratic equation is `1/(18 - x) - 1/(18 + x) = 1/24`

`=> ((18 + x) - (18 - x))/((18 + x) (18 - x)) = 1/24`

`=> (2x)/(18^2 - x^2) = 1/24`

`=>` 48x + 324 – x²

`=>` x² + 48x – 324 = 0

`=>` x² + 54x − 6x − 324 = 0

`=>` x(x + 54) − 6(x + 54) = 0

`=>` (x + 54)(x − 6) = 0

`=>` x = −54 or x = 6

But as x > 0, so x can't be negative.

Hence, x = 6