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\frac{\left(2x+1\right)\left(x+2\right)}{\left(x^{2}-4\right)\left(x-5\right)}
Multiply \frac{2x+1}{x^{2}-4} times \frac{x+2}{x-5} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x+2\right)\left(2x+1\right)}{\left(x-5\right)\left(x-2\right)\left(x+2\right)}
Factor the expressions that are not already factored.
\frac{2x+1}{\left(x-5\right)\left(x-2\right)}
Cancel out x+2 in both numerator and denominator.
\frac{2x+1}{x^{2}-7x+10}
Expand the expression.
\frac{\left(2x+1\right)\left(x+2\right)}{\left(x^{2}-4\right)\left(x-5\right)}
Multiply \frac{2x+1}{x^{2}-4} times \frac{x+2}{x-5} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x+2\right)\left(2x+1\right)}{\left(x-5\right)\left(x-2\right)\left(x+2\right)}
Factor the expressions that are not already factored.
\frac{2x+1}{\left(x-5\right)\left(x-2\right)}
Cancel out x+2 in both numerator and denominator.
\frac{2x+1}{x^{2}-7x+10}
Expand the expression.