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

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

Solve for x

$$x=5\left(\sqrt{3}-1\right)\approx 3.660254038$$

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.

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

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

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

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

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

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

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