Question 158890
Assume the problem is:
{{{((x^2 - 12x + 32))/((x^2 - 6x -16))}}}
--------------
{{{((x^2-x-12))/((x^2-5x-24))}}}
:
First remember your grade school rules on fractions:
"Invert the dividing fraction and multiply", so we have:
{{{((x^2 - 12x + 32))/((x^2 - 6x -16))}}} *  {{{((x^2-5x-24))/((x^2-x-12))}}}
:
Factor as much as we can and see what we have:
{{{((x-8)(x-4))/((x-8)(x+2))}}} *  {{{((x-8)(x+3))/((x-4)(x+3))}}}
:
Two of the (x-8)'s will cancel, (x-4)'s will cancel, we then have
{{{1/((x+2))}}} *  {{{((x-8)(x+3))/((x+3))}}}
;
Do the same with (x+3)'s
{{{1/((x+2))}}} *  (x-8) = {{{((x-8))/((x+2))}}}
:
did this makes sense to you? has your sanity been preserved?  Hope so!