Question 147743

{{{((x^2-5x+6)/(x^2+x-6))((x^2-4)/(x^2-x-6))}}} Start with the given expression.



{{{(((x-2)*(x-3))/(x^2+x-6))((x^2-4)/(x^2-x-6))}}} Factor {{{x^2-5x+6}}} to get {{{(x-2)*(x-3)}}}.



{{{(((x-2)*(x-3))/((x+3)*(x-2)))((x^2-4)/(x^2-x-6))}}} Factor {{{x^2+x-6}}} to get {{{(x+3)*(x-2)}}}.



{{{(((x-2)*(x-3))/((x+3)*(x-2)))(((x-2)*(x+2))/(x^2-x-6))}}} Factor {{{x^2-4}}} to get {{{(x-2)*(x+2)}}}.



{{{(((x-2)*(x-3))/((x+3)*(x-2)))(((x-2)*(x+2))/((x+2)*(x-3)))}}} Factor {{{x^2-x-6}}} to get {{{(x+2)*(x-3)}}}.



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



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



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



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



So {{{((x^2-5x+6)/(x^2+x-6))((x^2-4)/(x^2-x-6))}}} simplifies to {{{(x-2)/(x+3)}}}.



In other words, {{{((x^2-5x+6)/(x^2+x-6))((x^2-4)/(x^2-x-6))=(x-2)/(x+3)}}} where {{{x<>-3}}}, {{{x<>-2}}}, or {{{x<>2}}}