Question

Simplify
6/x-2 + 3/2+x - 9x-5/x^2+x-6

Answer 1

Assuming the usual carelessness with parentheses, Let's go with
6/(x-2) + 3/(2+x) - (9x-5)/(x^2+x-6)
= 6/(x-2) + 3/(x+2) - (9x-5)/((x+3)(x-2))
Now, that's ok, but something tells me you really meant
6/(x-2) + 3/(x+3) - (9x-5)/((x+3)(x-2))
which makes our common denominator (x+3)(x-2). Using that, we have
(6(x+3) + 3(x-2) - (9x-5)) / ((x+3)(x-2))
= 17/(x^2+x-6)
If I read things wrong, I'm sure you can follow my logic to make the necessary corrections...