Solve x^3-2x^2/x^2-1div(x-1-2x-1/x+1)

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

Evaluate

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

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}.

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

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

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

Do the multiplications in \left(x-1\right)\left(x+1\right)-\left(2x-1\right).

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

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

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

Divide \frac{x^{3}-2x^{2}}{x^{2}-1} by \frac{x^{2}-2x}{x+1} by multiplying \frac{x^{3}-2x^{2}}{x^{2}-1} by the reciprocal of \frac{x^{2}-2x}{x+1}.

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

Factor the expressions that are not already factored.

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

Cancel out x\left(x-2\right)\left(x+1\right) in both numerator and denominator.

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

Expand

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

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}.

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

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

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

Do the multiplications in \left(x-1\right)\left(x+1\right)-\left(2x-1\right).

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

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

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

Divide \frac{x^{3}-2x^{2}}{x^{2}-1} by \frac{x^{2}-2x}{x+1} by multiplying \frac{x^{3}-2x^{2}}{x^{2}-1} by the reciprocal of \frac{x^{2}-2x}{x+1}.

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

Factor the expressions that are not already factored.

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

Cancel out x\left(x-2\right)\left(x+1\right) in both numerator and denominator.

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