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\frac{\frac{x}{x}-\frac{1}{x}}{x-\frac{1}{x}}
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-\frac{1}{x}}
Since \frac{x}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x-1}{x}}{\frac{xx}{x}-\frac{1}{x}}
To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.
\frac{\frac{x-1}{x}}{\frac{xx-1}{x}}
Since \frac{xx}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x-1}{x}}{\frac{x^{2}-1}{x}}
Do the multiplications in xx-1.
\frac{\left(x-1\right)x}{x\left(x^{2}-1\right)}
Divide \frac{x-1}{x} by \frac{x^{2}-1}{x} by multiplying \frac{x-1}{x} by the reciprocal of \frac{x^{2}-1}{x}.
\frac{x-1}{x^{2}-1}
Cancel out x in both numerator and denominator.
\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{\frac{x}{x}-\frac{1}{x}}{x-\frac{1}{x}}
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-\frac{1}{x}}
Since \frac{x}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x-1}{x}}{\frac{xx}{x}-\frac{1}{x}}
To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.
\frac{\frac{x-1}{x}}{\frac{xx-1}{x}}
Since \frac{xx}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x-1}{x}}{\frac{x^{2}-1}{x}}
Do the multiplications in xx-1.
\frac{\left(x-1\right)x}{x\left(x^{2}-1\right)}
Divide \frac{x-1}{x} by \frac{x^{2}-1}{x} by multiplying \frac{x-1}{x} by the reciprocal of \frac{x^{2}-1}{x}.
\frac{x-1}{x^{2}-1}
Cancel out x in both numerator and denominator.
\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.