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

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,2 since division by zero is not defined. Multiply both sides of the equation by x\left(x-2\right), the least common multiple of x^{2}-2x,x,x-2.

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

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

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

Use the distributive property to multiply x-2 by x-1 and combine like terms.

$$1+x^{2}-3x+2=x^{2}$$

Add 1 and 2 to get 3.

$$3+x^{2}-3x=x^{2}$$

Subtract x^{2} from both sides.

$$3+x^{2}-3x-x^{2}=0$$

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

$$3-3x=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$-3x=-3$$

Divide both sides by -3.

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

Divide -3 by -3 to get 1.

$$x=1$$