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

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

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

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+2,x.

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

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

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

Use the distributive property to multiply x+2 by 2x-1 and combine like terms.

$$x^{2}\times 2=2x^{2}+3x-2$$

Subtract 2x^{2} from both sides.

$$x^{2}\times 2-2x^{2}=3x-2$$

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

$$0=3x-2$$

Swap sides so that all variable terms are on the left hand side.

$$3x-2=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$3x=2$$

Divide both sides by 3.

$$x=\frac{2}{3}$$