SOLUTION: Before I go completely insane, would somebody help me with this expression? x^2 - 12x + 32/x^2 - 6x -16 divided by x^2-x-12/x^2-5x-24 thank you. Please help.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Before I go completely insane, would somebody help me with this expression? x^2 - 12x + 32/x^2 - 6x -16 divided by x^2-x-12/x^2-5x-24 thank you. Please help.      Log On


   

Question 158890: Before I go completely insane, would somebody help me with this expression?
x^2 - 12x + 32/x^2 - 6x -16 divided by x^2-x-12/x^2-5x-24
thank you. Please help.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the problem is:
%28%28x%5E2+-+12x+%2B+32%29%29%2F%28%28x%5E2+-+6x+-16%29%29
--------------
%28%28x%5E2-x-12%29%29%2F%28%28x%5E2-5x-24%29%29
:
First remember your grade school rules on fractions:
"Invert the dividing fraction and multiply", so we have:
%28%28x%5E2+-+12x+%2B+32%29%29%2F%28%28x%5E2+-+6x+-16%29%29 * %28%28x%5E2-5x-24%29%29%2F%28%28x%5E2-x-12%29%29
:
Factor as much as we can and see what we have:
%28%28x-8%29%28x-4%29%29%2F%28%28x-8%29%28x%2B2%29%29 * %28%28x-8%29%28x%2B3%29%29%2F%28%28x-4%29%28x%2B3%29%29
:
Two of the (x-8)'s will cancel, (x-4)'s will cancel, we then have
1%2F%28%28x%2B2%29%29 * %28%28x-8%29%28x%2B3%29%29%2F%28%28x%2B3%29%29
;
Do the same with (x+3)'s
1%2F%28%28x%2B2%29%29 * (x-8) = %28%28x-8%29%29%2F%28%28x%2B2%29%29
:
did this makes sense to you? has your sanity been preserved? Hope so!