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\frac{x-5}{3x+6}\times \frac{2\left(x+2\right)}{2\left(x-5\right)}
Factor the expressions that are not already factored in \frac{2x+4}{2x-10}.
\frac{x-5}{3x+6}\times \frac{x+2}{x-5}
Cancel out 2 in both numerator and denominator.
\frac{\left(x-5\right)\left(x+2\right)}{\left(3x+6\right)\left(x-5\right)}
Multiply \frac{x-5}{3x+6} times \frac{x+2}{x-5} by multiplying numerator times numerator and denominator times denominator.
\frac{x+2}{3x+6}
Cancel out x-5 in both numerator and denominator.
\frac{x+2}{3\left(x+2\right)}
Factor the expressions that are not already factored.
\frac{1}{3}
Cancel out x+2 in both numerator and denominator.