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Differentiate w.r.t. m
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\frac{m^{2}-81}{\left(m+9\right)\times 4}
Divide \frac{1}{m+9} by \frac{4}{m^{2}-81} by multiplying \frac{1}{m+9} by the reciprocal of \frac{4}{m^{2}-81}.
\frac{\left(m-9\right)\left(m+9\right)}{4\left(m+9\right)}
Factor the expressions that are not already factored.
\frac{m-9}{4}
Cancel out m+9 in both numerator and denominator.