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

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Subtract 2x^{2} from both sides.

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

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

$$x+1=2x$$

Subtract 2x from both sides.

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

Combine x and -2x to get -x.

$$-x+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-x=-1$$

Multiply both sides by -1.

$$x=1$$