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

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

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,0 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,x+2.

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

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

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

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.

$$x+2=2x$$

Subtract 2x from 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.

$$-x=-2$$

Multiply both sides by -1.

$$x=2$$