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