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Differentiate w.r.t. k
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\frac{k^{2}-4}{\left(k+2\right)\times 5}
Divide \frac{1}{k+2} by \frac{5}{k^{2}-4} by multiplying \frac{1}{k+2} by the reciprocal of \frac{5}{k^{2}-4}.
\frac{\left(k-2\right)\left(k+2\right)}{5\left(k+2\right)}
Factor the expressions that are not already factored.
\frac{k-2}{5}
Cancel out k+2 in both numerator and denominator.