Question 150930
{{{((x^2+3x-10)/(x+3))/((x^2-x-2)/(x+1))}}} Start with the given expression.



{{{((x^2+3x-10)/(x+3))((x+1)/(x^2-x-2))}}} Multiply the first fraction {{{(x^2+3x-10)/(x+3)}}} by the reciprocal of the second fraction {{{(x^2-x-2)/(x+1)}}}.



{{{(((x+5)(x-2))/(x+3))((x+1)/(x^2-x-2))}}} Factor {{{x^2+3x-10}}} to get {{{(x+5)*(x-2)}}}.



{{{(((x+5)(x-2))/(x+3))((x+1)/((x+1)(x-2)))}}} Factor {{{x^2-x-2}}} to get {{{(x+1)*(x-2)}}}.



{{{((x+5)(x-2)(x+1))/((x+3)(x+1)(x-2))}}} Combine the fractions. 



{{{((x+5)highlight((x-2))highlight((x+1)))/((x+3)highlight((x+1))highlight((x-2)))}}} Highlight the common terms. 



{{{((x+5)cross((x-2))cross((x+1)))/((x+3)cross((x+1))cross((x-2)))}}} Cancel out the common terms. 



{{{(x+5)/(x+3)}}} Simplify. 



So {{{((x^2+3x-10)/(x+3))/((x^2-x-2)/(x+1))}}} simplifies to {{{(x+5)/(x+3)}}}.



In other words, {{{((x^2+3x-10)/(x+3))/((x^2-x-2)/(x+1))=(x+5)/(x+3)}}} where {{{x<>-3}}}, {{{x<>-1}}}, or {{{x<>2}}}