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\frac{\left(1+\frac{1}{x}\right)x}{x^{2}-1}
Divide 1+\frac{1}{x} by \frac{x^{2}-1}{x} by multiplying 1+\frac{1}{x} by the reciprocal of \frac{x^{2}-1}{x}.
\frac{\left(\frac{x}{x}+\frac{1}{x}\right)x}{x^{2}-1}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.
\frac{\frac{x+1}{x}x}{x^{2}-1}
Since \frac{x}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.
\frac{x+1}{x^{2}-1}
Cancel out x and x.
\frac{x+1}{\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored.
\frac{1}{x-1}
Cancel out x+1 in both numerator and denominator.
\frac{\left(1+\frac{1}{x}\right)x}{x^{2}-1}
Divide 1+\frac{1}{x} by \frac{x^{2}-1}{x} by multiplying 1+\frac{1}{x} by the reciprocal of \frac{x^{2}-1}{x}.
\frac{\left(\frac{x}{x}+\frac{1}{x}\right)x}{x^{2}-1}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.
\frac{\frac{x+1}{x}x}{x^{2}-1}
Since \frac{x}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.
\frac{x+1}{x^{2}-1}
Cancel out x and x.
\frac{x+1}{\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored.
\frac{1}{x-1}
Cancel out x+1 in both numerator and denominator.