Solve frac{x^{3}+x}{x^2-x}-x^3-x^2/x^2-2x+1

$$\frac { x ^ { 3 } + x } { x ^ { 2 } - x } - \frac { x ^ { 3 } - x ^ { 2 } } { x ^ { 2 } - 2 x + 1 }$$

Evaluate

$$\frac{1}{x-1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{3}+x}{x^{2}-x}.

$$\frac{x\left(x^{2}+1\right)}{x\left(x-1\right)}-\frac{x^{3}-x^{2}}{x^{2}-2x+1}$$

Cancel out x in both numerator and denominator.

$$\frac{x^{2}+1}{x-1}-\frac{x^{3}-x^{2}}{x^{2}-2x+1}$$

Factor the expressions that are not already factored in \frac{x^{3}-x^{2}}{x^{2}-2x+1}.

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

Cancel out x-1 in both numerator and denominator.

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

Since \frac{x^{2}+1}{x-1} and \frac{x^{2}}{x-1} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{1}{x-1}$$

Expand

$$\frac{1}{x-1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{3}+x}{x^{2}-x}.

$$\frac{x\left(x^{2}+1\right)}{x\left(x-1\right)}-\frac{x^{3}-x^{2}}{x^{2}-2x+1}$$

Cancel out x in both numerator and denominator.

$$\frac{x^{2}+1}{x-1}-\frac{x^{3}-x^{2}}{x^{2}-2x+1}$$

Factor the expressions that are not already factored in \frac{x^{3}-x^{2}}{x^{2}-2x+1}.

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

Cancel out x-1 in both numerator and denominator.

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

Since \frac{x^{2}+1}{x-1} and \frac{x^{2}}{x-1} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{1}{x-1}$$