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\frac{\left(x+1\right)^{3}}{x^{2}-1}
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
\frac{\left(x+1\right)^{3}}{\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored.
\frac{\left(x+1\right)^{2}}{x-1}
Cancel out x+1 in both numerator and denominator.
\frac{x^{2}+2x+1}{x-1}
Expand the expression.
\frac{\left(x+1\right)^{3}}{x^{2}-1}
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
\frac{\left(x+1\right)^{3}}{\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored.
\frac{\left(x+1\right)^{2}}{x-1}
Cancel out x+1 in both numerator and denominator.
\frac{x^{2}+2x+1}{x-1}
Expand the expression.