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