Solve x=frac{sqrt{6}-sqrt{3}}{sqrt{3}}

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

Solve for x

$$x=\sqrt{2}-1\approx 0.414213562$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{\sqrt{6}-\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Use the distributive property to multiply \sqrt{6}-\sqrt{3} by \sqrt{3}.

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

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

The square of \sqrt{3} is 3.

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

Divide each term of 3\sqrt{2}-3 by 3 to get \sqrt{2}-1.

$$x=\sqrt{2}-1$$

Assign x

$$x≔\sqrt{2}-1$$