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\frac{x+1}{x+3}\times \frac{\left(x-6\right)\left(x+6\right)}{\left(x-6\right)\left(x+1\right)}
Factor the expressions that are not already factored in \frac{x^{2}-36}{x^{2}-5x-6}.
\frac{x+1}{x+3}\times \frac{x+6}{x+1}
Cancel out x-6 in both numerator and denominator.
\frac{\left(x+1\right)\left(x+6\right)}{\left(x+3\right)\left(x+1\right)}
Multiply \frac{x+1}{x+3} times \frac{x+6}{x+1} by multiplying numerator times numerator and denominator times denominator.
\frac{x+6}{x+3}
Cancel out x+1 in both numerator and denominator.
\frac{x+1}{x+3}\times \frac{\left(x-6\right)\left(x+6\right)}{\left(x-6\right)\left(x+1\right)}
Factor the expressions that are not already factored in \frac{x^{2}-36}{x^{2}-5x-6}.
\frac{x+1}{x+3}\times \frac{x+6}{x+1}
Cancel out x-6 in both numerator and denominator.
\frac{\left(x+1\right)\left(x+6\right)}{\left(x+3\right)\left(x+1\right)}
Multiply \frac{x+1}{x+3} times \frac{x+6}{x+1} by multiplying numerator times numerator and denominator times denominator.
\frac{x+6}{x+3}
Cancel out x+1 in both numerator and denominator.