Question 240635
{{{( (x^2 + x - 6) / (x^2 - x + 12) ) / ( (x^2 + x - 20) / (x^2 - 4x + 4) )}}}


Invert the denominator and multiply:
{{{( (x^2 + x - 6) / (x^2 - x + 12) ) * ( (x^2 -4x +4) / (x^2 +x-20) )}}}


Now, FACTOR, FACTOR, FACTOR:
{{{ ((x+3)(x-2))/(x^2-x+12)}}}*{{{((x-2)^2)/((x+5)(x-4)) )}}}


Strangely enough, the first denominator does NOT factor (are you sure you didn't copy this wrong???), and no factors divide out.  The final answer here is really UGLY, and I doubt if it is correct.

{{{((x+3)*(x-2)^3)/((x^2-x+12)*(x+5)*(x-4))}}}


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus