SOLUTION: {{{((x-6)/(x^2-x-6))-((x+3)/(x^2+8x+12))}}} I'm having so much trouble with this question, nothing is working for me.

Question 283066: I'm having so much trouble with this question, nothing is working for me.
Found 2 solutions by richwmiller, mananth:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Just looking at it I would suspect that (x-6) and/or (x+3) are factors of the denominators.
Answer :
or Answer:
How did I get there?
Start with

The long way:
multiply first fraction by and the second fraction by aka to make a common denominator
=
multiply it out =
collect terms =
add =
rearrange
Answer:
or
Answer :
Another way to to do the same thing:
The short way:

multiply by
multiply by

multiply out the numerators
and get the same as above.
Answer :

Answer by mananth(16949) (Show Source): You can put this solution on YOUR website!

(x-6)/(x^2-6x+x-6) - (x+3) / x^2+6x+2x+12)
(x-6)/ {x(x-6)+1(x-6)} - (x+3) / {x(x+6)+2(x+6)}
(x-6) / (x+1)(x-6) - (x+3)/(x+6)(x+2)
1/ (x+1) - (x+3) / (x+6)(x+2)
(x+6)(x+2) - (x+1)(x+3) / (x+1)(x+6)(x+2)
(x^2+8x+12) - (x^2+4x+3) / (x+1)((x+6)(x+2)
(x^2+8x+12-x^2-4x-3)/(x+1((x+6)(x+2)
(4x-9)/(x+1)(x+6)(x+2)