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\frac{\left(x-6\right)\left(x+6\right)}{x^{2}-12x+36}
Divide x-6 by \frac{x^{2}-12x+36}{x+6} by multiplying x-6 by the reciprocal of \frac{x^{2}-12x+36}{x+6}.
\frac{\left(x-6\right)\left(x+6\right)}{\left(x-6\right)^{2}}
Factor the expressions that are not already factored.
\frac{x+6}{x-6}
Cancel out x-6 in both numerator and denominator.
\frac{\left(x-6\right)\left(x+6\right)}{x^{2}-12x+36}
Divide x-6 by \frac{x^{2}-12x+36}{x+6} by multiplying x-6 by the reciprocal of \frac{x^{2}-12x+36}{x+6}.
\frac{\left(x-6\right)\left(x+6\right)}{\left(x-6\right)^{2}}
Factor the expressions that are not already factored.
\frac{x+6}{x-6}
Cancel out x-6 in both numerator and denominator.