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Differentiate w.r.t. g
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\frac{g^{2}-49}{\left(g+7\right)\times 3}
Divide \frac{1}{g+7} by \frac{3}{g^{2}-49} by multiplying \frac{1}{g+7} by the reciprocal of \frac{3}{g^{2}-49}.
\frac{\left(g-7\right)\left(g+7\right)}{3\left(g+7\right)}
Factor the expressions that are not already factored.
\frac{g-7}{3}
Cancel out g+7 in both numerator and denominator.