Question 971728

I am dividing Rational expression by another rational expression and am getting stuck. Here is the situation:
the problem: x^2+3x-28/x^2-36 divided by x^2-13x+36/x^2+11x+30

After inverting the dividend, I followed the steps and ended up with
(x-7)(x-4)/(x-9)(x+4) times (x+6)(x+5)/(x-9)(x-4)
After cancelling out (x-4), I'm stuck.
The answer key has an answer of
(x-7)(x+5)/(x-6)(x-9) How did they get that answer if there is still (x+5) and (x+4) still in the equation?
<pre>This is how:
{{{(x^2 + 3x - 28)/(x^2 - 36)}}}{{{"÷"}}}{{{(x^2 - 13x + 36)/(x^2 + 11x + 30)}}}
{{{(x + 7)(x - 4)/(x - 6)(x + 6)}}}{{{"÷"}}}{{{(x - 9)(x - 4)/(x + 5)(x + 6)}}} ------ Factoring numerators and denominators
{{{(x + 7)(x - 4)/(x - 6)(x + 6)}}}{{{"*"}}}{{{(x + 5)(x + 6)/(x - 9)(x - 4)}}} ------ Changing division to multiplication and inverting DIVISOR
{{{(x + 7)cross((x - 4))/(x - 6)cross((x + 6))}}}{{{"*"}}}{{{(x + 5)cross((x + 6))/(x - 9)cross((x - 4))}}} ----- Canceling numerators and denominators
{{{((x + 7)(x + 5))/((x - 6)(x - 9))}}}, or {{{highlight_green(highlight_green((x^2 + 12x + 35)/(x^2 - 15x + 54)))}}}
You should be able to determine where you went wrong!!