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

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

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

Subtract \frac{x^{2}+2x-2}{x-1} from both sides.

$$x-\frac{x^{2}+2x-2}{x-1}=0$$

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

$$\frac{x\left(x-1\right)}{x-1}-\frac{x^{2}+2x-2}{x-1}=0$$

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

$$\frac{x\left(x-1\right)-\left(x^{2}+2x-2\right)}{x-1}=0$$

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

$$\frac{x^{2}-x-x^{2}-2x+2}{x-1}=0$$

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

$$\frac{-3x+2}{x-1}=0$$

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.

$$-3x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-3x=-2$$

Divide both sides by -3.

$$x=\frac{-2}{-3}$$

Fraction \frac{-2}{-3} can be simplified to \frac{2}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{2}{3}$$