Question 193655




{{{((x^2-4x-60)/(x+6))((x-6)/(x^2+3x-54))}}} Start with the given expression.



{{{(((x+6)*(x-10))/(x+6))((x-6)/(x^2+3x-54))}}} Factor {{{x^2-4x-60}}} to get {{{(x+6)*(x-10)}}}.



{{{(((x+6)(x-10))/((x+6)))(((x-6))/((x+9)(x-6)))}}} Factor {{{x^2+3x-54}}} to get {{{(x+9)*(x-6)}}}.



{{{((x+6)(x-10)(x-6))/((x+6)(x+9)(x-6))}}} Combine the fractions. 




{{{(highlight((x+6))(x-10)highlight((x-6)))/(highlight((x+6))(x+9)highlight((x-6)))}}} Highlight the common terms. 




{{{(cross((x+6))(x-10)cross((x-6)))/(cross((x+6))(x+9)cross((x-6)))}}} Cancel out the common terms. 



{{{(x-10)/(x+9)}}} Simplify. 



So {{{((x^2-4x-60)/(x+6))((x-6)/(x^2+3x-54))}}} simplifies to {{{(x-10)/(x+9)}}}.



In other words, {{{((x^2-4x-60)/(x+6))((x-6)/(x^2+3x-54))=(x-10)/(x+9)}}} where {{{x<>-9}}}, {{{x<>-6}}}, or {{{x<>6}}}