Solve frac{sqrt{3}}{3}=x/x+200

$$\frac { \sqrt { 3 } } { 3 } = \frac { x } { x + 200 }$$

Solve for x

$$x=100\left(\sqrt{3}+1\right)\approx 273.205080757$$

Steps for Solving Linear Equation

Variable x cannot be equal to -200 since division by zero is not defined. Multiply both sides of the equation by 3\left(x+200\right), the least common multiple of 3,x+200.

$$\left(x+200\right)\sqrt{3}=3x$$

Use the distributive property to multiply x+200 by \sqrt{3}.

$$x\sqrt{3}+200\sqrt{3}=3x$$

Subtract 3x from both sides.

$$x\sqrt{3}+200\sqrt{3}-3x=0$$

Subtract 200\sqrt{3} from both sides. Anything subtracted from zero gives its negation.

$$x\sqrt{3}-3x=-200\sqrt{3}$$

Combine all terms containing x.

$$\left(\sqrt{3}-3\right)x=-200\sqrt{3}$$

Divide both sides by \sqrt{3}-3.

$$\frac{\left(\sqrt{3}-3\right)x}{\sqrt{3}-3}=-\frac{200\sqrt{3}}{\sqrt{3}-3}$$

Dividing by \sqrt{3}-3 undoes the multiplication by \sqrt{3}-3.

$$x=-\frac{200\sqrt{3}}{\sqrt{3}-3}$$

Divide -200\sqrt{3} by \sqrt{3}-3.

$$x=100\sqrt{3}+100$$