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\frac{x^{2}-64}{x+8}
Since \frac{x^{2}}{x+8} and \frac{64}{x+8} have the same denominator, subtract them by subtracting their numerators.
\frac{\left(x-8\right)\left(x+8\right)}{x+8}
Factor the expressions that are not already factored in \frac{x^{2}-64}{x+8}.
x-8
Cancel out x+8 in both numerator and denominator.