Solve 2/3x+2/sqrt{3}=

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

Evaluate

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

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

Use the distributive property to multiply \frac{2}{3}x+2 by \sqrt{3}.

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

Factor

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

Solution Steps

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

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

The square of \sqrt{3} is 3.

$$factor(\frac{\left(\frac{2}{3}x+2\right)\sqrt{3}}{3})$$

Use the distributive property to multiply \frac{2}{3}x+2 by \sqrt{3}.

$$factor(\frac{\frac{2}{3}x\sqrt{3}+2\sqrt{3}}{3})$$

Consider \frac{2}{3}x\times 3^{\frac{1}{2}}+2\times 3^{\frac{1}{2}}. Factor out \frac{2}{3}.

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

Consider x\sqrt{3}+3^{\frac{3}{2}}. Factor out \sqrt{3}.

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

Rewrite the complete factored expression. Simplify.

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