How do you subtract \frac { x ^ { 2} - 10x } { x ^ { 2} - 11x - 12} - \frac { 24} { x ^ { 2} - 11x - 12}?

1 Answer
Jun 7, 2017

It's (x+2)/(x+1).

Explanation:

Let's start with the original problem:

(x^2-10x)/(x^2-11x-12)-(24)/(x^2-11x-12)

Noting that the two fractions have common denominators, we can simplify the expression as so:

(x^2-10x-24)/(x^2-11x-12)

Then, we can factor both the numerator and the denominator into a (x+a)(x+b) format:

((x+2)(x-12))/((x+1)(x-12))

Then, we cancel the x-12s and finish the problem with the final answer:

(x+2)/(x+1)