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

Step-by-step explanation:

`(1)/(x-6) = (3x+12)/(x^(2)-6x) -(6x-24)/(x^(2)-6x)`

`(1)/(x-6) = (3x+12)/(x(x-6)) -(6x-24)/(x(x-6))`

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

`(x(x-6)1)/(x-6) = (x(x-6)3x+12)/(x(x-6)) -(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