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

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Answer 1 · 2017-06-07T05:45:46

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

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-12#s and finish the problem with the final answer:

#(x+2)/(x+1)#