Question

Solve the following quadratic equations by factorization:

${\displaystyle \frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}}$ , x ≠ 4, 7

Answer 1

We have been given

${\displaystyle \frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}}$

${\displaystyle \frac{-11}{x^2-3x-28}=\frac{11}{30}}$

-30 = x² - 3x - 28

x² - 3x - 28 + 30 = 0

x² - 3x + 2 = 0

x² - 2x - x + 2 = 0

x(x - 2) - 1(x - 2) = 0

(x - 1)(x - 2) = 0

Therefore,

x - 1 = 0

x = 1

or,

x - 2 = 0

x = 2

Hence, x = 1 or x = 2.