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

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

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

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,x-1.

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

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

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

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

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

Subtract 2x^{2} from both sides.

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

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

$$x-1=-2x$$

Add 2x to both sides.

$$x-1+2x=0$$

Combine x and 2x to get 3x.

$$3x-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$3x=1$$

Divide both sides by 3.

$$x=\frac{1}{3}$$