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