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

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

Evaluate

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

Short Solution Steps

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

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

Cancel out x in both numerator and denominator.

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

Extract the negative sign in 1-x^{2}.

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

Cancel out x^{2}-1 in both numerator and denominator.

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

The opposite of -1 is 1.

$$\frac{1}{x+1}+1$$

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

$$\frac{1}{x+1}+\frac{x+1}{x+1}$$

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

$$\frac{1+x+1}{x+1}$$

Combine like terms in 1+x+1.

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

Expand

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

Short Solution Steps

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

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

Cancel out x in both numerator and denominator.

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

Extract the negative sign in 1-x^{2}.

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

Cancel out x^{2}-1 in both numerator and denominator.

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

The opposite of -1 is 1.

$$\frac{1}{x+1}+1$$

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

$$\frac{1}{x+1}+\frac{x+1}{x+1}$$

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

$$\frac{1+x+1}{x+1}$$

Combine like terms in 1+x+1.

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