Question

Remember to check for extraneous solutions 1/(x-6)=(3x+12)/(x^2-6x) - (6x-24)/(x^2-6x) A) {-1} B) {9} C) {-3} D) {3,-3}

Answer 1

Answer: B

Explanation:

$\frac{1}{x-6} = \frac{3x+12}{x^{2}-6x} -\frac{6x-24}{x^{2}-6x}$

$\frac{1}{x-6} = \frac{3x+12}{x(x-6)} -\frac{6x-24}{x(x-6)}$

RESTRICTIONS: x(x-6)≠0  ⇒ x ≠ 0 and x ≠ 6

$\frac{x(x-6)1}{x-6} = \frac{x(x-6)3x+12}{x(x-6)} -\frac{x(x-6)6x-24}{x(x-6)}$

x = 3x + 12 - (6x - 24)

x = 3x + 12 - 6x + 24

x = -3x + 36

4x = 36

x = 9