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