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

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

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$xx-2\left(x-1\right)=xx+x\left(-1\right)$$

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

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

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

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

Use the distributive property to multiply -2 by x-1.

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

Subtract x^{2} from both sides.

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

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

$$-2x+2=x\left(-1\right)$$

Subtract x\left(-1\right) from both sides.

$$-2x+2-x\left(-1\right)=0$$

Combine -2x and -x\left(-1\right) to get -x.

$$-x+2=0$$

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

$$-x=-2$$

Multiply both sides by -1.

$$x=2$$