Skip to main content
Evaluate
Tick mark Image
Expand
Tick mark Image
Graph

Similar Problems from Web Search

Share

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