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

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

Solve for x (complex solution)

$$x\in \mathrm{C}\setminus 1,0$$

Solution Steps

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^{2}-x.

$$x\times 2x=2x^{2}$$

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

$$x^{2}\times 2=2x^{2}$$

Subtract 2x^{2} from both sides.

$$x^{2}\times 2-2x^{2}=0$$

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

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Variable x cannot be equal to any of the values 1,0.

$$x\in \mathrm{C}\setminus 0,1$$

Solve for x

$$x\in \mathrm{R}\setminus 1,0$$

Solution Steps

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^{2}-x.

$$x\times 2x=2x^{2}$$

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

$$x^{2}\times 2=2x^{2}$$

Subtract 2x^{2} from both sides.

$$x^{2}\times 2-2x^{2}=0$$

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

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Variable x cannot be equal to any of the values 1,0.

$$x\in \mathrm{R}\setminus 0,1$$