Solve x/10+x=frac{sqrt{3}}{3}

$$\frac{ x }{ 10+x } = \frac{ \sqrt{ 3 } }{ 3 }$$

Solve for x

$$x=5\left(\sqrt{3}+1\right)\approx 13.660254038$$

Steps for Solving Linear Equation

Variable x cannot be equal to -10 since division by zero is not defined. Multiply both sides of the equation by 3\left(x+10\right), the least common multiple of 10+x,3.

$$3x=\left(x+10\right)\sqrt{3}$$

Use the distributive property to multiply x+10 by \sqrt{3}.

$$3x=x\sqrt{3}+10\sqrt{3}$$

Subtract x\sqrt{3} from both sides.

$$3x-x\sqrt{3}=10\sqrt{3}$$

Reorder the terms.

$$-\sqrt{3}x+3x=10\sqrt{3}$$

Combine all terms containing x.

$$\left(-\sqrt{3}+3\right)x=10\sqrt{3}$$

The equation is in standard form.

$$\left(3-\sqrt{3}\right)x=10\sqrt{3}$$

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

$$\frac{\left(3-\sqrt{3}\right)x}{3-\sqrt{3}}=\frac{10\sqrt{3}}{3-\sqrt{3}}$$

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

$$x=\frac{10\sqrt{3}}{3-\sqrt{3}}$$

Divide 10\sqrt{3} by -\sqrt{3}+3.

$$x=5\sqrt{3}+5$$