Solve (1/x-1+x+1):(x^2/1-2x+x^2)

$$( \frac { 1 } { x - 1 } + x + 1 ) : ( \frac { x ^ { 2 } } { 1 - 2 x + x ^ { 2 } } )$$

Evaluate

$$x-1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x+1 times \frac{x-1}{x-1}.

$$\frac{\frac{1}{x-1}+\frac{\left(x+1\right)\left(x-1\right)}{x-1}}{\frac{x^{2}}{1-2x+x^{2}}}$$

Since \frac{1}{x-1} and \frac{\left(x+1\right)\left(x-1\right)}{x-1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+\left(x+1\right)\left(x-1\right)}{x-1}}{\frac{x^{2}}{1-2x+x^{2}}}$$

Do the multiplications in 1+\left(x+1\right)\left(x-1\right).

$$\frac{\frac{1+x^{2}-x+x-1}{x-1}}{\frac{x^{2}}{1-2x+x^{2}}}$$

Combine like terms in 1+x^{2}-x+x-1.

$$\frac{\frac{x^{2}}{x-1}}{\frac{x^{2}}{1-2x+x^{2}}}$$

Divide \frac{x^{2}}{x-1} by \frac{x^{2}}{1-2x+x^{2}} by multiplying \frac{x^{2}}{x-1} by the reciprocal of \frac{x^{2}}{1-2x+x^{2}}.

$$\frac{x^{2}\left(1-2x+x^{2}\right)}{\left(x-1\right)x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{x^{2}-2x+1}{x-1}$$

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.

$$x-1$$

Expand

$$x-1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x+1 times \frac{x-1}{x-1}.

$$\frac{\frac{1}{x-1}+\frac{\left(x+1\right)\left(x-1\right)}{x-1}}{\frac{x^{2}}{1-2x+x^{2}}}$$

Since \frac{1}{x-1} and \frac{\left(x+1\right)\left(x-1\right)}{x-1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+\left(x+1\right)\left(x-1\right)}{x-1}}{\frac{x^{2}}{1-2x+x^{2}}}$$

Do the multiplications in 1+\left(x+1\right)\left(x-1\right).

$$\frac{\frac{1+x^{2}-x+x-1}{x-1}}{\frac{x^{2}}{1-2x+x^{2}}}$$

Combine like terms in 1+x^{2}-x+x-1.

$$\frac{\frac{x^{2}}{x-1}}{\frac{x^{2}}{1-2x+x^{2}}}$$

Divide \frac{x^{2}}{x-1} by \frac{x^{2}}{1-2x+x^{2}} by multiplying \frac{x^{2}}{x-1} by the reciprocal of \frac{x^{2}}{1-2x+x^{2}}.

$$\frac{x^{2}\left(1-2x+x^{2}\right)}{\left(x-1\right)x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{x^{2}-2x+1}{x-1}$$

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.

$$x-1$$