Solve x(x+1)/x-2+x(1-x)/x-2

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Expand

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

Short Solution Steps

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

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

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

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

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

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