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

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

Solve for x

$$x=-2$$

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,x.

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

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

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

To find the opposite of x-2, find the opposite of each term.

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

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

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

Subtract x^{2} from both sides.

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

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

$$-x+2=-2x$$

Add 2x to both sides.

$$-x+2+2x=0$$

Combine -x and 2x to get x.

$$x+2=0$$

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

$$x=-2$$