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\frac{\left(a^{2}-3a\right)\left(a^{2}-1\right)}{\left(a^{2}+a\right)\left(a-3\right)}\times \frac{a+1}{a-1}
Divide \frac{a^{2}-3a}{a^{2}+a} by \frac{a-3}{a^{2}-1} by multiplying \frac{a^{2}-3a}{a^{2}+a} by the reciprocal of \frac{a-3}{a^{2}-1}.
\frac{a\left(a-3\right)\left(a-1\right)\left(a+1\right)}{a\left(a-3\right)\left(a+1\right)}\times \frac{a+1}{a-1}
Factor the expressions that are not already factored in \frac{\left(a^{2}-3a\right)\left(a^{2}-1\right)}{\left(a^{2}+a\right)\left(a-3\right)}.
\left(a-1\right)\times \frac{a+1}{a-1}
Cancel out a\left(a-3\right)\left(a+1\right) in both numerator and denominator.
a+1
Cancel out a-1 and a-1.
\frac{\left(a^{2}-3a\right)\left(a^{2}-1\right)}{\left(a^{2}+a\right)\left(a-3\right)}\times \frac{a+1}{a-1}
Divide \frac{a^{2}-3a}{a^{2}+a} by \frac{a-3}{a^{2}-1} by multiplying \frac{a^{2}-3a}{a^{2}+a} by the reciprocal of \frac{a-3}{a^{2}-1}.
\frac{a\left(a-3\right)\left(a-1\right)\left(a+1\right)}{a\left(a-3\right)\left(a+1\right)}\times \frac{a+1}{a-1}
Factor the expressions that are not already factored in \frac{\left(a^{2}-3a\right)\left(a^{2}-1\right)}{\left(a^{2}+a\right)\left(a-3\right)}.
\left(a-1\right)\times \frac{a+1}{a-1}
Cancel out a\left(a-3\right)\left(a+1\right) in both numerator and denominator.
a+1
Cancel out a-1 and a-1.