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

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

Evaluate

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

Short Solution Steps

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

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

Cancel out x in both numerator and denominator.

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

To find the opposite of x+1, find the opposite of each term.

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

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

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

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

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

Do the multiplications in x^{2}+2x-1+\left(-x-1\right)\left(x+1\right).

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

Combine like terms in x^{2}+2x-1-x^{2}-x-x-1.

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

Expand

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

Short Solution Steps

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

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

Cancel out x in both numerator and denominator.

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

To find the opposite of x+1, find the opposite of each term.

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

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

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

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

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

Do the multiplications in x^{2}+2x-1+\left(-x-1\right)\left(x+1\right).

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

Combine like terms in x^{2}+2x-1-x^{2}-x-x-1.

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