Question 168527
{{{(3a^2-9a-12)/(6a^2+30a+24)}}} Start with the given expression



{{{(3(a-4)(a+1))/(6a^2+30a+24)}}} Factor the numerator



{{{(3(a-4)(a+1))/(6(a+4)(a+1))}}} Factor the denominator



{{{(3(a-4)highlight((a+1)))/(6(a+4)highlight((a+1)))}}} Highlight the common terms.



{{{(3(a-4)cross((a+1)))/(6(a+4)cross((a+1)))}}} Cancel out the common 



{{{(3(a-4))/(6(a+4))}}} Simplify



{{{(a-4)/(2(a+4))}}} Reduce



{{{(a-4)/(2a+8)}}} Distribute



So {{{(3a^2-9a-12)/(6a^2+30a+24)}}} simplifies to {{{(a-4)/(2a+8)}}} 



In other words, {{{(3a^2-9a-12)/(6a^2+30a+24)=(a-4)/(2a+8)}}}  where {{{a<>-4}}} or {{{a<>-1}}}