Question

(x)/(x-3)-4-(2x-5)/(x+2)

I posted something before this, so now this is how far I got.
The answer I know is -(5x^2-17x-9)/(x-3)(x+2)

first I get

(x)(x+2)/(x-3)(x+2)- (4)(x-3)(x+2)/(x-3)(x+2)-(2x-5)(x-3)/(x-3)(x+2)
Then I get

x^2+2x-4x^2-4x-24-2x^2-11x+15 (for the top)

When I put everything together I get

(-5x^2 -13x -9)/ (x-3)(x+2)

as you can see however I am having a problem with + and - because I get -13x instead of -17x so could you look at what I am doing wrong and explain it to me?

The top should be this:

x^2 + 2x - 4x^2 + 4x + 24 - 2x^2 + 11x - 15

Combining like terms:

-5x^2 + 17x + 9

Factoring out the negative gives this:

-(5x^2 - 17x - 9)

This should help you see the answer given:

-(5x^2-17x-9)/(x-3)(x+2)

I hope this helps. Watch those negative signs because they can be tricky on these types of problems!