Question 142861
{{{((3w+18)/(w^2-36))/((w^2+3w-18)/(w^2-3w-18))}}} Start with the given expression


{{{((3w+18)/(w^2-36))*((w^2-3w-18)/(w^2+3w-18))}}} Multiply the first fraction by the reciprocal of the second fraction



{{{((3(w+6))/(w^2-36))((w^2-3w-18)/(w^2+3w-18))}}}   Factor {{{3w+18}}} to get {{{3(w+6)}}} 


{{{((3(w+6))/((w+6)(w-6)))((w^2-3w-18)/(w^2+3w-18))}}}   Factor {{{w^2-36}}} to get {{{(w+6)(w-6)}}} 


{{{((3(w+6))/((w+6)(w-6)))(((w-6)(w+3))/(w^2+3w-18))}}}   Factor {{{w^2-3w-18}}} to get {{{(w-6)(w+3)}}} 


{{{((3(w+6))/((w+6)(w-6)))(((w-6)(w+3))/((w+6)(w-3)))}}}   Factor {{{w^2+3w-18}}} to get {{{(w+6)(w-3)}}} 



{{{(3(w+6)(w-6)(w+3))/(w+6)(w-6)(w+6)(w-3)}}} Combine the fractions



{{{(3highlight((w+6))highlight((w-6))(w+3))/highlight((w+6))highlight((w-6))(w+6)(w-3)}}} Highlight like terms



{{{(3cross((w+6))cross((w-6))(w+3))/cross((w+6))cross((w-6))(w+6)(w-3)}}} Cancel like terms



{{{(3(w+3))/(w+6)(w-3)}}} Simplify



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Answer:


So {{{((3w+18)/(w^2-36))((w^2-3w-18)/(w^2+3w-18))}}} simplifies to {{{(3(w+3))/(w+6)(w-3)}}}.