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