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

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

Solve for x

$$x = -\frac{3 \sqrt{2}}{2} \approx -2.121320344$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{x}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{x\sqrt{3}}{\left(\sqrt{3}\right)^{2}}=x\sqrt{3}+\sqrt{6}$$

The square of \sqrt{3} is 3.

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

Subtract x\sqrt{3} from both sides.

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

Combine \frac{x\sqrt{3}}{3} and -x\sqrt{3} to get -\frac{2}{3}x\sqrt{3}.

$$-\frac{2}{3}x\sqrt{3}=\sqrt{6}$$

The equation is in standard form.

$$\left(-\frac{2\sqrt{3}}{3}\right)x=\sqrt{6}$$

Divide both sides by -\frac{2}{3}\sqrt{3}.

$$\frac{\left(-\frac{2\sqrt{3}}{3}\right)x}{-\frac{2\sqrt{3}}{3}}=\frac{\sqrt{6}}{-\frac{2\sqrt{3}}{3}}$$

Dividing by -\frac{2}{3}\sqrt{3} undoes the multiplication by -\frac{2}{3}\sqrt{3}.

$$x=\frac{\sqrt{6}}{-\frac{2\sqrt{3}}{3}}$$

Divide \sqrt{6} by -\frac{2}{3}\sqrt{3}.

$$x=-\frac{3\sqrt{2}}{2}$$