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\frac{x^{2}+12x-\left(12x+36\right)}{x+6}
Since \frac{x^{2}+12x}{x+6} and \frac{12x+36}{x+6} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+12x-12x-36}{x+6}
Do the multiplications in x^{2}+12x-\left(12x+36\right).
\frac{x^{2}-36}{x+6}
Combine like terms in x^{2}+12x-12x-36.
\frac{\left(x-6\right)\left(x+6\right)}{x+6}
Factor the expressions that are not already factored in \frac{x^{2}-36}{x+6}.
x-6
Cancel out x+6 in both numerator and denominator.
\frac{x^{2}+12x-\left(12x+36\right)}{x+6}
Since \frac{x^{2}+12x}{x+6} and \frac{12x+36}{x+6} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+12x-12x-36}{x+6}
Do the multiplications in x^{2}+12x-\left(12x+36\right).
\frac{x^{2}-36}{x+6}
Combine like terms in x^{2}+12x-12x-36.
\frac{\left(x-6\right)\left(x+6\right)}{x+6}
Factor the expressions that are not already factored in \frac{x^{2}-36}{x+6}.
x-6
Cancel out x+6 in both numerator and denominator.
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