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\frac{x^{2}-25}{x+5}
Since \frac{x^{2}}{x+5} and \frac{25}{x+5} have the same denominator, subtract them by subtracting their numerators.
\frac{\left(x-5\right)\left(x+5\right)}{x+5}
Factor the expressions that are not already factored in \frac{x^{2}-25}{x+5}.
x-5
Cancel out x+5 in both numerator and denominator.