Question 120642

{{{(x^2-15x+54)/(x^2-36)}}} Start with the given expression


{{{((x-9)(x-6))/(x^2-36)}}}   Factor {{{x^2-15x+54}}} to get {{{(x-9)(x-6)}}} 


{{{((x-9)(x-6))/((x+6)(x-6))}}}   Factor {{{x^2-36}}} to get {{{(x+6)(x-6)}}} 




{{{(x-9)cross((x-6))/(x+6)cross((x-6))}}} Cancel like terms



{{{(x-9)/(x+6)}}} Simplify



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Answer:


So {{{(x^2-15x+54)/(x^2-36)}}} simplifies to {{{(x-9)/(x+6)}}}. In other words {{{(x^2-15x+54)/(x^2-36)=(x-9)/(x+6)}}}