Solve -x/x+frac{1{x-2}}

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Use the distributive property to multiply -x by x-2.

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

Differentiate w.r.t. x

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