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\frac{a^{2}-9}{a-3}
Since \frac{a^{2}}{a-3} and \frac{9}{a-3} have the same denominator, subtract them by subtracting their numerators.
\frac{\left(a-3\right)\left(a+3\right)}{a-3}
Factor the expressions that are not already factored in \frac{a^{2}-9}{a-3}.
a+3
Cancel out a-3 in both numerator and denominator.