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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Differentiate w.r.t. x

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