Question 118916


{{{(x^2-13x+42)/(x^2-36)}}} Start with the given expression


{{{((x-7)(x-6))/(x^2-36)}}}   Factor {{{x^2-13x+42}}} to get {{{(x-7)(x-6)}}} 


{{{((x-7)(x-6))/((x+6)(x-6))}}}   Factor {{{x^2-36}}} to get {{{(x+6)(x-6)}}} 



{{{(x-7)(x-6)/(x+6)(x-6)}}} Combine the fractions



{{{(x-7)cross((x-6))/(x+6)cross((x-6))}}} Cancel like terms



{{{(x-7)/(x+6)}}} Simplify



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Answer:


So {{{(x^2-13x+42)/(x^2-36)}}} simplifies to {{{(x-7)/(x+6)}}}. In other words {{{(x^2-13x+42)/(x^2-36)=(x-7)/(x+6)}}}