Solve x+4/x=x/x+4

$$\frac{ x+4 }{ x } = \frac{ x }{ x+4 }$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+4\right), the least common multiple of x,x+4.

$$\left(x+4\right)\left(x+4\right)=xx$$

Multiply x+4 and x+4 to get \left(x+4\right)^{2}.

$$\left(x+4\right)^{2}=xx$$

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

$$\left(x+4\right)^{2}=x^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$x^{2}+8x+16=x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+8x+16-x^{2}=0$$

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

$$8x+16=0$$

Subtract 16 from both sides. Anything subtracted from zero gives its negation.

$$8x=-16$$

Divide both sides by 8.

$$x=\frac{-16}{8}$$

Divide -16 by 8 to get -2.

$$x=-2$$