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

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

Evaluate

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

Short Solution Steps

Combine x^{2} and -x^{2} to get 0.

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

Anything divided by one gives itself.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x}{x}.

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

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

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x+1 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

Combine x^{2} and -x^{2} to get 0.

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

Anything divided by one gives itself.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x}{x}.

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

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

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x+1 in both numerator and denominator.

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

Expand the expression.

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