Solve 2x/x+2+3/x=2

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

Solve for x

$$x=6$$

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.

$$x\times 2x+\left(x+2\right)\times 3=2x\left(x+2\right)$$

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

$$x^{2}\times 2+\left(x+2\right)\times 3=2x\left(x+2\right)$$

Use the distributive property to multiply x+2 by 3.

$$x^{2}\times 2+3x+6=2x\left(x+2\right)$$

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

$$x^{2}\times 2+3x+6=2x^{2}+4x$$

Subtract 2x^{2} from both sides.

$$x^{2}\times 2+3x+6-2x^{2}=4x$$

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

$$3x+6=4x$$

Subtract 4x from both sides.

$$3x+6-4x=0$$

Combine 3x and -4x to get -x.

$$-x+6=0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-x=-6$$

Multiply both sides by -1.

$$x=6$$