Solve frac{sqrt{3}x}{100+x}=frac{sqrt{3}}{3}

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

Solve for x

$$x=50$$

Steps for Solving Linear Equation

Variable x cannot be equal to -100 since division by zero is not defined. Multiply both sides of the equation by 3\left(x+100\right), the least common multiple of 100+x,3.

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

Use the distributive property to multiply x+100 by \sqrt{3}.

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

Subtract x\sqrt{3} from both sides.

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

Combine 3\sqrt{3}x and -x\sqrt{3} to get 2\sqrt{3}x.

$$2\sqrt{3}x=100\sqrt{3}$$

Divide both sides by 2\sqrt{3}.

$$\frac{2\sqrt{3}x}{2\sqrt{3}}=\frac{100\sqrt{3}}{2\sqrt{3}}$$

Dividing by 2\sqrt{3} undoes the multiplication by 2\sqrt{3}.

$$x=\frac{100\sqrt{3}}{2\sqrt{3}}$$

Divide 100\sqrt{3} by 2\sqrt{3}.

$$x=50$$