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\frac{\left(a-1\right)\left(a^{2}-4\right)}{\left(a+2\right)\left(a-1\right)^{2}}
Multiply \frac{a-1}{a+2} times \frac{a^{2}-4}{\left(a-1\right)^{2}} by multiplying numerator times numerator and denominator times denominator.
\frac{a^{2}-4}{\left(a-1\right)\left(a+2\right)}
Cancel out a-1 in both numerator and denominator.
\frac{\left(a-2\right)\left(a+2\right)}{\left(a-1\right)\left(a+2\right)}
Factor the expressions that are not already factored.
\frac{a-2}{a-1}
Cancel out a+2 in both numerator and denominator.
\frac{\left(a-1\right)\left(a^{2}-4\right)}{\left(a+2\right)\left(a-1\right)^{2}}
Multiply \frac{a-1}{a+2} times \frac{a^{2}-4}{\left(a-1\right)^{2}} by multiplying numerator times numerator and denominator times denominator.
\frac{a^{2}-4}{\left(a-1\right)\left(a+2\right)}
Cancel out a-1 in both numerator and denominator.
\frac{\left(a-2\right)\left(a+2\right)}{\left(a-1\right)\left(a+2\right)}
Factor the expressions that are not already factored.
\frac{a-2}{a-1}
Cancel out a+2 in both numerator and denominator.