Question

Solve the following quadratic equations by factorization:

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

Answer 1

We have been given

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

2(x² + 1 - 2x + 4x² + 1 + 4x) = 5(2x² - x - 1)

10x² + 4x + 4 = 10x² - 5x - 5

9x + 9 = 0

Therefore,

9x = -9

x = -9/9

x = -1

Hence, x = -1