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

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

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

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

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

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

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

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

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

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

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

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

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

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2.

$$-2x+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-2x=-1$$

Divide both sides by -2.

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

Fraction \frac{-1}{-2} can be simplified to \frac{1}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1}{2}$$