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\frac{2\left(2x-1\right)\left(x+1\right)\left(\frac{1}{2}x+1\right)}{2\left(x+1\right)}
Factor the expressions that are not already factored.
\left(2x-1\right)\left(\frac{1}{2}x+1\right)
Cancel out 2\left(x+1\right) in both numerator and denominator.
x^{2}+\frac{3}{2}x-1
Expand the expression.
\frac{2\left(2x-1\right)\left(x+1\right)\left(\frac{1}{2}x+1\right)}{2\left(x+1\right)}
Factor the expressions that are not already factored.
\left(2x-1\right)\left(\frac{1}{2}x+1\right)
Cancel out 2\left(x+1\right) in both numerator and denominator.
x^{2}+\frac{3}{2}x-1
Expand the expression.