Solve 3*x^2-1/x+1divx^2-2x+1/x^2-x

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

Evaluate

$$3x$$

Short Solution Steps

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

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

Cancel out x+1 in both numerator and denominator.

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

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

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

Cancel out x-1 in both numerator and denominator.

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

Divide 3\left(x-1\right) by \frac{x-1}{x} by multiplying 3\left(x-1\right) by the reciprocal of \frac{x-1}{x}.

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

Cancel out x-1 in both numerator and denominator.

$$3x$$

Expand

$$3x$$

Short Solution Steps

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

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

Cancel out x+1 in both numerator and denominator.

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

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

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

Cancel out x-1 in both numerator and denominator.

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

Divide 3\left(x-1\right) by \frac{x-1}{x} by multiplying 3\left(x-1\right) by the reciprocal of \frac{x-1}{x}.

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

Cancel out x-1 in both numerator and denominator.

$$3x$$