Solve frac{2sqrt{3}-sqrt{2}}{2sqrt{3}+sqrt{3}}

$$\frac { 2 \sqrt { 3 } - \sqrt { 2 } } { 2 \sqrt { 3 } + \sqrt { 3 } }$$

Evaluate

$$-\frac{\sqrt{6}}{9}+\frac{2}{3}\approx 0.39450114$$

Solution Steps

Combine 2\sqrt{3} and \sqrt{3} to get 3\sqrt{3}.

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

Rationalize the denominator of \frac{2\sqrt{3}-\sqrt{2}}{3\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{\left(2\sqrt{3}-\sqrt{2}\right)\sqrt{3}}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{\left(2\sqrt{3}-\sqrt{2}\right)\sqrt{3}}{9}$$

Use the distributive property to multiply 2\sqrt{3}-\sqrt{2} by \sqrt{3}.

$$\frac{2\left(\sqrt{3}\right)^{2}-\sqrt{2}\sqrt{3}}{9}$$

The square of \sqrt{3} is 3.

$$\frac{2\times 3-\sqrt{2}\sqrt{3}}{9}$$

Multiply 2 and 3 to get 6.

$$\frac{6-\sqrt{2}\sqrt{3}}{9}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{6-\sqrt{6}}{9}$$

Factor

$$\frac{\sqrt{6} {(\sqrt{6} - 1)}}{9} = 0.3945011396907579$$