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

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

Evaluate

$$\frac{x^{3}+x^{2}-x+1}{x+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}-1 times \frac{x+1}{x+1}.

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

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

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

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

$$\frac{x^{3}+x^{2}-x-1+2}{x+1}$$

Combine like terms in x^{3}+x^{2}-x-1+2.

$$\frac{x^{3}+x^{2}-x+1}{x+1}$$

Differentiate w.r.t. x

$$\frac{2\left(x^{3}+2x^{2}+x-1\right)}{\left(x+1\right)^{2}}$$