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\frac{\left(a^{2}-5a+6\right)\times 6a}{\left(3a-15\right)\left(a^{2}-a-30\right)}
Multiply \frac{a^{2}-5a+6}{3a-15} times \frac{6a}{a^{2}-a-30} by multiplying numerator times numerator and denominator times denominator.
\frac{6a\left(a-3\right)\left(a-2\right)}{3\left(a-6\right)\left(a-5\right)\left(a+5\right)}
Factor the expressions that are not already factored.
\frac{2a\left(a-3\right)\left(a-2\right)}{\left(a-6\right)\left(a-5\right)\left(a+5\right)}
Cancel out 3 in both numerator and denominator.
\frac{2a^{3}-10a^{2}+12a}{a^{3}-6a^{2}-25a+150}
Expand the expression.
\frac{\left(a^{2}-5a+6\right)\times 6a}{\left(3a-15\right)\left(a^{2}-a-30\right)}
Multiply \frac{a^{2}-5a+6}{3a-15} times \frac{6a}{a^{2}-a-30} by multiplying numerator times numerator and denominator times denominator.
\frac{6a\left(a-3\right)\left(a-2\right)}{3\left(a-6\right)\left(a-5\right)\left(a+5\right)}
Factor the expressions that are not already factored.
\frac{2a\left(a-3\right)\left(a-2\right)}{\left(a-6\right)\left(a-5\right)\left(a+5\right)}
Cancel out 3 in both numerator and denominator.
\frac{2a^{3}-10a^{2}+12a}{a^{3}-6a^{2}-25a+150}
Expand the expression.