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

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

Evaluate

$$x$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and 1-x is x-1. Multiply \frac{x}{1-x} times \frac{-1}{-1}.

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

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

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

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

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

Cancel out x-1 in both numerator and denominator.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and 1-x is x-1. Multiply \frac{x}{1-x} times \frac{-1}{-1}.

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

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

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

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.

$$1$$