Question

Solve the following quadratic equations by factorization:

`(x + 3)/(x - 2) - (1 - x)/x = 17/4; x ≠ 0, 2`

Answer 1

We have been given

`(x+3)/(x-2)-(1-x)/x=17/4`

4(x² + 3x - x + x² + 2 - 2x) = 17(x² - 2x)

9x² - 34x - 8 = 0

9x² - 36x + 2x - 8 = 0

9x(x - 4) + 2(x - 4) = 0

(9x + 2)(x - 4) = 0

Therefore,

9x + 2 = 0

9x = -2

x = `(-2)/9`

or,

x - 4 = 0

x = 4

Hence, x = `(-2)/9` or x = 4.