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