Question 710748
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.
{{{((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)))}}}
So we are good up to here. But with
{{{((r+4)/((r-3)(r-4))) * (((r-4)(r-3))/((r+2)(r+4)))}}}
we have inverted the wrong fraction. It should be:
{{{(((r-3)(r-4))/(r+4))*(((r+2)(r+4))/((r-4)(r-3)))}}}
After canceling we get:
{{{(r+2)/1}}}
which simplifies to just:
r+2