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

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

Solve for x

$$x=5\sqrt{3}+15\approx 23.660254038$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x, the least common multiple of x,3.

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

Use the distributive property to multiply 3 by x-10.

$$3x-30=x\sqrt{3}$$

Subtract x\sqrt{3} from both sides.

$$3x-30-x\sqrt{3}=0$$

Add 30 to both sides. Anything plus zero gives itself.

$$3x-x\sqrt{3}=30$$

Combine all terms containing x.

$$\left(3-\sqrt{3}\right)x=30$$

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

$$\frac{\left(3-\sqrt{3}\right)x}{3-\sqrt{3}}=\frac{30}{3-\sqrt{3}}$$

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

$$x=\frac{30}{3-\sqrt{3}}$$

Divide 30 by 3-\sqrt{3}.

$$x=5\sqrt{3}+15$$