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\frac{z^{2}-36}{z+6}
Since \frac{z^{2}}{z+6} and \frac{36}{z+6} have the same denominator, subtract them by subtracting their numerators.
\frac{\left(z-6\right)\left(z+6\right)}{z+6}
Factor the expressions that are not already factored in \frac{z^{2}-36}{z+6}.
z-6
Cancel out z+6 in both numerator and denominator.