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