SOLUTION: Please describe and correct the error: (r^2-7r+12/r+4)/(r^2-7r+12/r^2+6r+8)= {(r-3)(r-4)/r+4)}/(r-4)(r-3)/(r+2)(r+4) = r+4/(r-3)(r-4)x (r-4)(r-3)/(r+2)(r+4)= 1/r+2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please describe and correct the error: (r^2-7r+12/r+4)/(r^2-7r+12/r^2+6r+8)= {(r-3)(r-4)/r+4)}/(r-4)(r-3)/(r+2)(r+4) = r+4/(r-3)(r-4)x (r-4)(r-3)/(r+2)(r+4)= 1/r+2      Log On


   

Question 710748: Please describe and correct the error:
(r^2-7r+12/r+4)/(r^2-7r+12/r^2+6r+8)= {(r-3)(r-4)/r+4)}/(r-4)(r-3)/(r+2)(r+4) =
r+4/(r-3)(r-4)x (r-4)(r-3)/(r+2)(r+4)= 1/r+2
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The error is that when the division was changed to a multiplication, the first fraction was inverted. It should be the second fraction (only) that gets inverted.
%28%28r%5E2-7r%2B12%29%2F%28r%2B4%29%29%2F%28%28r%5E2-7r%2B12%29%2F%28r%5E2%2B6r%2B8%29%29

So we are good up to here. But with

we have inverted the wrong fraction. It should be:

After canceling we get:
%28r%2B2%29%2F1
which simplifies to just:
r+2