Question

I am having trouble with this.

Add (simplify if possible)

(x^2 + 11x)/(x^2 - 3x) + (x^2 - 6x)/(x^2 - 3x)

I actully came up with two possible answers.

(2x+5)/x-3 and (2x^2-5)/x-6x

I'm not sure which answer is correct.

Answer 1

The denominators of the two added terms can be written x(x-3). The x^2-6x term can be written x(x-6). Therefore
(x^2 + 11x)/(x^2 - 3x) + (x^2 - 6x)/(x^2 - 3x) = [x(x+11) + x(x-6)]/[(x(x-3)]
Cancel out the x terms and you get
(2x-5)/(x-3)