Question 77107
{{{((w^2+2w)/(w^2-9))/((w^2+7w+10)/(w^2+8w+15))}}}




{{{(w(w+2)/(w^2-9))/((w^2+7w+10)/(w^2+8w+15))}}} Factor w out of the numerator

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Factor the denominator {{{(w^2-9)}}}

*[invoke factoring_quadratics 1, 0, -9]

So the denominator {{{(w^2-9)}}} factors to:
{{{(w-3)(w+3)}}}

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Factor the numerator {{{(w^2+7w+10)}}}

*[invoke factoring_quadratics 1, 7, 10]


So the numerator {{{w^2+7w+10}}} factors to:
{{{(w+2)(w+5)}}}

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Factor the denominator {{{(w^2+8w+15)}}}

*[invoke factoring_quadratics 1, 8, 15]


So the denominator {{{w^2+8w+15}}} factors to:
{{{(w+3)(w+5)}}}

So the whole expression becomes


{{{(w(w+2)/((w-3)(w+3)))/(((w+2)(w+5))/((w+3)(w+5)))}}}




{{{(w*cross((w+2))/((w-3)cross((w+3))))*((cross((w+3))cross((w+5)))/(cross((w+2))cross((w+5))))}}}

Which reduces to:

{{{w/(w-3)}}}