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\frac{z^{2}-49}{z+7}
Since \frac{z^{2}}{z+7} and \frac{49}{z+7} have the same denominator, subtract them by subtracting their numerators.
\frac{\left(z-7\right)\left(z+7\right)}{z+7}
Factor the expressions that are not already factored in \frac{z^{2}-49}{z+7}.
z-7
Cancel out z+7 in both numerator and denominator.