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

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

Evaluate

$$x+1$$

Short Solution Steps

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

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

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

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

Combine like terms in x-1+1.

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

$$x+1$$

Expand

$$x+1$$

Short Solution Steps

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

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

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

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

Combine like terms in x-1+1.

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

$$x+1$$