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.

Algebra ->  Square-cubic-other-roots -> 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.      Log On


   

Question 283066: %28%28x-6%29%2F%28x%5E2-x-6%29%29-%28%28x%2B3%29%2F%28x%5E2%2B8x%2B12%29%29 I'm having so much trouble with this question, nothing is working for me.
Found 2 solutions by richwmiller, mananth:
Answer by richwmiller(17219) About Me  (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 :-27%2F%28%28x-3%29+%28x%2B2%29+%28x%2B6%29%29
or Answer:+-27%2F%28x%5E3%2B5x%5E2-12x-36%29+
How did I get there?
Start with
%28%28x-6%29%2F%28x%5E2-x-6%29%29-%28%28x%2B3%29%2F%28x%5E2%2B8x%2B12%29%29
The long way:
multiply first fraction by %286%2Bx%29%2F%286%2Bx%29 and the second fraction by %28x-3%29%2F%28x-3%29 aka %28-3%2Bx%29%2F%28-3%2Bx%29 to make a common denominator
=
multiply it out =
collect terms = %28-36%2Bx%5E2+%2B+9-x%5E2%29%2F%28-36-12x%2B5x%5E2%2Bx%5E3%29+
add =-27%2F%28-36-12+x%2B5+x%5E2%2Bx%5E3%29+
rearrange
Answer:+-27%2F%28x%5E3%2B5x%5E2-12x-36%29+
or
Answer :-27%2F%28%28x-3%29+%28x%2B2%29+%28x%2B6%29%29
Another way to to do the same thing:
The short way:
x%5E2-x-6=%28x-3%29%28x%2B2%29
x%5E2%2B8x%2B12=%28x%2B6%29%28x%2B2%29
%28%28x-6%29%2F%28x%5E2-x-6%29%29-%28%28x%2B3%29%2F%28x%5E2%2B8x%2B12%29%29
%28%28x-6%29%2F%28x-3%29%28x%2B2%29%29-%28%28x%2B3%29%2F%28x%2B6%29%28x%2B2%29%29
multiply by %286%2Bx%29%2F%286%2Bx%29
multiply by %28x-3%29%2F%28x-3%29

multiply out the numerators
and get the same as above.
Answer :-27%2F%28%28x-3%29+%28x%2B2%29+%28x%2B6%29%29

Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x-6%29%2F%28x%5E2-x-6%29%29-%28%28x%2B3%29%2F%28x%5E2%2B8x%2B12%29%29
(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)