Solve x/x-1=x-1/x

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

Solve for x

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

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,1 since division by zero is not defined. Multiply both sides of the equation by x\left(x-1\right), the least common multiple of x-1,x.

$$xx=\left(x-1\right)\left(x-1\right)$$

Multiply x and x to get x^{2}.

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

Multiply x-1 and x-1 to get \left(x-1\right)^{2}.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

Subtract x^{2} from both sides.

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

Combine x^{2} and -x^{2} to get 0.

$$0=-2x+1$$

Swap sides so that all variable terms are on the left hand side.

$$-2x+1=0$$

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.

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