Question

Solve the following equation:

`1/("x" - 1) - 1/"x" = 1/("x" + 3) - 1/("x" + 4)`

Answer 1

`1/("x" - 1) - 1/"x" = 1/("x" + 3) - 1/("x" + 4)`

`=> ("x" - ("x" - 1))/(("x" - 1)"x") = (("x" + 4)-("x" + 3))/(("x" + 3)("x" + 4))`

`= 1/(("x" - 1)"x") = 1/(("x" + 3)("x" + 4))`

= (x + 3)(x + 4) = x(x - 1)

⇒ x² + 4x + 3x + 12 = x² - x

⇒ x² + 7x - x² + x = -12 

8x = -12

x = `-12/8 = - 3/2 = - 1 1/2`