Question 127503
{{{((a^2 - 1)/(a^2 - 2a -15))((2a + 6)/(a^2 - a))}}} Start with the given expression


{{{(((a+1)(a-1))/(a^2 - 2a -15))((2a + 6)/(a^2 - a))}}}   Factor {{{a^2 - 1}}} to get {{{(a+1)(a-1)}}} 


{{{(((a+1)(a-1))/((a-5)(a+3)))((2a + 6)/(a^2 - a))}}}   Factor {{{a^2 - 2a -15}}} to get {{{(a-5)(a+3)}}} 


{{{(((a+1)(a-1))/((a-5)(a+3)))((2(a+3))/(a^2 - a))}}}   Factor {{{2a + 6}}} to get {{{2(a+3)}}} 


{{{(((a+1)(a-1))/((a-5)(a+3)))((2(a+3))/(a(a-1)))}}}   Factor {{{a^2 - a}}} to get {{{a(a-1)}}} 



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


{{{(a+1)cross(a-1)2cross(a+3)/((a-5)cross(a+3)a*cross(a-1))}}} Cancel like terms


{{{2(a+1)/a(a-5)}}} Simplify




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Answer:



So {{{((a^2 - 1)/(a^2 - 2a -15))((2a + 6)/(a^2 - a))}}} simplifies to {{{2(a+1)/a(a-5)}}}



In other words,  {{{((a^2 - 1)/(a^2 - 2a -15))((2a + 6)/(a^2 - a))=2(a+1)/a(a-5)}}}