Question

Solve the following equation by factorization

`x/(x - 1) + (x - 1)/x = 2(1)/(2)`

Answer 1

`x/(x - 1) + (x - 1)/x = 2(1)/(2)`

`x/(x - 1) + (x - 1)/x = (5)/(2)`

⇒ `(x^2 + x^2 - 2x + 1)/(x(x - 1)) = (5)/(2)`

⇒ `(2x^2 - 2x + 1)/(x(x - 1)) = (5)/(2)`

⇒ 4x² - 4x + 2 = 5x² - 5x
⇒ 4x² - 4x + 2 - 5x² + 5x = 0
⇒ -x² + x + 2 = 0 
⇒ x² - x - 2 = 0
⇒ x² - 2x + x - 2 = 0
⇒ x(x - 2) + 1(x - 2) = 0
⇒ (x - 2) (x + 1) = 0
Either x - 2 = 0,
then x = 2
or
x + 1 = 0,
then x = -1
Hence x = 2, -1.