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

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

Evaluate

$$x$$

Short Solution Steps

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

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

Cancel out x-1 in both numerator and denominator.

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

Multiply \frac{x^{2}-x}{x+1} times \frac{x+1}{x-1} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x+1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

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

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

Cancel out x-1 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}-x}{x+1}\times \frac{x+1}{x-1})$$

Multiply \frac{x^{2}-x}{x+1} times \frac{x+1}{x-1} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x+1 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}-x}{x-1})$$

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

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

Cancel out x-1 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

The derivative of ax^{n} is nax^{n-1}.

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

For any term t except 0, t^{0}=1.

$$1$$