Question 145770


{{{(x^2+x-12)/(9-x^2)}}} Start with the given expression.



{{{((x+4)*(x-3))/(9-x^2)}}} Factor {{{x^2+x-12}}} to get {{{(x+4)*(x-3)}}}.



{{{((x+4)*(x-3))/(-(x-3)*(x+3))}}} Factor {{{9-x^2}}} to get {{{-(x-3)*(x+3)}}}.



{{{-((x+4)highlight(x-3))/(highlight(x-3)(x+3))}}} Highlight the common terms. 



{{{-((x+4)cross(x-3))/(cross(x-3)(x+3))}}} Cancel out the common terms. 



{{{-((x+4))/((x+3))}}} Simplify. 



So {{{(x^2+x-12)/(9-x^2)}}} simplifies to {{{-((x+4))/((x+3))}}}.



In other words, {{{(x^2+x-12)/(9-x^2)=-((x+4))/((x+3))}}} where {{{x<>-3}}} or {{{x<>3}}}