Solve 3+(1/3x^2-3)/x=frac{sqrt{3}}{3}

$$\frac{ 3+( \frac{ 1 }{ 3 } { x }^{ 2 } -3) }{ x } = \frac{ \sqrt{ 3 } }{ 3 }$$

Solve for x

$$x=\sqrt{3}\approx 1.732050808$$

Steps Using Factoring

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.

$$3\left(3+\frac{1}{3}x^{2}-3\right)=x\sqrt{3}$$

Subtract 3 from 3 to get 0.

$$3\times \frac{1}{3}x^{2}=x\sqrt{3}$$

Multiply 3 and \frac{1}{3} to get 1.

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

Subtract x\sqrt{3} from both sides.

$$x^{2}-x\sqrt{3}=0$$

Reorder the terms.

$$x^{2}-\sqrt{3}x=0$$

Factor out x.

$$x\left(x-\sqrt{3}\right)=0$$

To find equation solutions, solve x=0 and x-\sqrt{3}=0.

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

Variable x cannot be equal to 0.

$$x=\sqrt{3}$$