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

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

Solve for x

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

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+2,x.

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

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

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

Use the distributive property to multiply x+2 by x+3 and combine like terms.

$$x^{2}=x^{2}+5x+6$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=5x+6$$

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

$$0=5x+6$$

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

$$5x+6=0$$

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

$$5x=-6$$

Divide both sides by 5.

$$x=\frac{-6}{5}$$

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$x=-\frac{6}{5}$$