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

$$\frac { 2 \times 1 / 3 \sqrt { 3 } } { 1 + ( 1 / 3 \sqrt { 3 } ) ^ { 2 } } =$$

Evaluate

$$\frac{\sqrt{3}}{2}\approx 0.866025404$$

Solution Steps

Multiply 2 and \frac{1}{3} to get \frac{2}{3}.

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

Expand \left(\frac{1}{3}\sqrt{3}\right)^{2}.

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

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{\frac{2}{3}\sqrt{3}}{1+\frac{1}{9}\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{2}{3}\sqrt{3}}{1+\frac{1}{9}\times 3}$$

Multiply \frac{1}{9} and 3 to get \frac{1}{3}.

$$\frac{\frac{2}{3}\sqrt{3}}{1+\frac{1}{3}}$$

Add 1 and \frac{1}{3} to get \frac{4}{3}.

$$\frac{\frac{2}{3}\sqrt{3}}{\frac{4}{3}}$$

Divide \frac{2}{3}\sqrt{3} by \frac{4}{3} by multiplying \frac{2}{3}\sqrt{3} by the reciprocal of \frac{4}{3}.

$$\frac{\frac{2}{3}\sqrt{3}\times 3}{4}$$

Multiply \frac{2}{3} and 3 to get 2.

$$\frac{2\sqrt{3}}{4}$$

Divide 2\sqrt{3} by 4 to get \frac{1}{2}\sqrt{3}.

$$\frac{1}{2}\sqrt{3}$$