Question 151406


{{{((x^2+x-12)/(x^2-x-20))((x^2+2x-35)/(x^2+9x+14))}}} Start with the given expression.



{{{(((x+4)*(x-3))/(x^2-x-20))((x^2+2x-35)/(x^2+9x+14))}}} Factor {{{x^2+x-12}}} to get {{{(x+4)*(x-3)}}}.



{{{(((x+4)*(x-3))/((x+4)*(x-5)))((x^2+2x-35)/(x^2+9x+14))}}} Factor {{{x^2-x-20}}} to get {{{(x+4)*(x-5)}}}.



{{{(((x+4)*(x-3))/((x+4)*(x-5)))(((x+7)*(x-5))/(x^2+9x+14))}}} Factor {{{x^2+2x-35}}} to get {{{(x+7)*(x-5)}}}.



{{{(((x+4)*(x-3))/((x+4)*(x-5)))(((x+7)*(x-5))/((x+7)*(x+2)))}}} Factor {{{x^2+9x+14}}} to get {{{(x+7)*(x+2)}}}.



{{{((x+4)*(x-3)(x+7)*(x-5))/((x+4)*(x-5)(x+7)*(x+2))}}} Combine the fractions. 



{{{(highlight((x+4))(x-3)highlight((x+7))highlight((x-5)))/(highlight((x+4))highlight((x-5))highlight((x+7))(x+2))}}} Highlight the common terms.



{{{(cross((x+4))(x-3)cross((x+7))cross((x-5)))/(cross((x+4))cross((x-5))cross((x+7))(x+2))}}} Cancel out the common terms.




{{{(x-3)/(x+2)}}} Simplify. 



So {{{((x^2+x-12)/(x^2-x-20))((x^2+2x-35)/(x^2+9x+14))}}} simplifies to {{{(x-3)/(x+2)}}}.



In other words, {{{((x^2+x-12)/(x^2-x-20))((x^2+2x-35)/(x^2+9x+14))=(x-3)/(x+2)}}} where {{{x<>-7}}}, {{{x<>-4}}}, {{{x<>-2}}}, or {{{x<>5}}}