Question

Find the root of the following equation.

`1/(x+4) - 1/(x-7) = 11/30, x ≠ -4, 7`

Answer 1

`1/(x+4) - 1/(x-7) = 11/30`

`⇒ (x-7-x-4)/((x+4)(x-7)) = 11/30`

`⇒ (-11)/((x+4)(x-7)) = 11/30`

⇒ (x + 4)(x − 7) = −30

⇒ x² − 3x − 28 = 30

⇒ x² − 3x + 2 = 0

⇒ x² − 2x − x + 2 = 0

⇒ x(x − 2) − 1(x − 2) = 0

⇒ (x − 2)(x − 1) = 0

⇒ x = 1 or 2