Solve frac{3sqrt{3}}{x}=6/6+x

$$\frac { 3 \sqrt { 3 } } { x } = \frac { 6 } { 6 + x }$$

Solve for x

$$x=12\sqrt{3}+18\approx 38.784609691$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -6,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+6\right), the least common multiple of x,6+x.

$$\left(x+6\right)\times 3\sqrt{3}=x\times 6$$

Use the distributive property to multiply x+6 by 3.

$$\left(3x+18\right)\sqrt{3}=x\times 6$$

Use the distributive property to multiply 3x+18 by \sqrt{3}.

$$3x\sqrt{3}+18\sqrt{3}=x\times 6$$

Subtract x\times 6 from both sides.

$$3x\sqrt{3}+18\sqrt{3}-x\times 6=0$$

Multiply -1 and 6 to get -6.

$$3x\sqrt{3}+18\sqrt{3}-6x=0$$

Subtract 18\sqrt{3} from both sides. Anything subtracted from zero gives its negation.

$$3x\sqrt{3}-6x=-18\sqrt{3}$$

Combine all terms containing x.

$$\left(3\sqrt{3}-6\right)x=-18\sqrt{3}$$

Divide both sides by 3\sqrt{3}-6.

$$\frac{\left(3\sqrt{3}-6\right)x}{3\sqrt{3}-6}=-\frac{18\sqrt{3}}{3\sqrt{3}-6}$$

Dividing by 3\sqrt{3}-6 undoes the multiplication by 3\sqrt{3}-6.

$$x=-\frac{18\sqrt{3}}{3\sqrt{3}-6}$$

Divide -18\sqrt{3} by 3\sqrt{3}-6.

$$x=12\sqrt{3}+18$$