Solve 2a-4/a^2+12a+36div10-5a/a^3+6a^2

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Polynomial

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\frac{\left(2a-4\right)\left(a^{3}+6a^{2}\right)}{\left(a^{2}+12a+36\right)\left(10-5a\right)}

Divide \frac{2a-4}{a^{2}+12a+36} by \frac{10-5a}{a^{3}+6a^{2}} by multiplying \frac{2a-4}{a^{2}+12a+36} by the reciprocal of \frac{10-5a}{a^{3}+6a^{2}}.

\frac{2\left(a-2\right)\left(a+6\right)a^{2}}{5\left(-a+2\right)\left(a+6\right)^{2}}

Factor the expressions that are not already factored.

\frac{-2\left(a+6\right)\left(-a+2\right)a^{2}}{5\left(-a+2\right)\left(a+6\right)^{2}}

Extract the negative sign in -2+a.

\frac{-2a^{2}}{5\left(a+6\right)}

Cancel out \left(a+6\right)\left(-a+2\right) in both numerator and denominator.

\frac{-2a^{2}}{5a+30}

Expand the expression.