Solve frac{1+sqrt{3}}{2}+frac{2-sqrt{3}}{3}=

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

Evaluate

$$\frac{\sqrt{3}+7}{6}\approx 1.455341801$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{1+\sqrt{3}}{2} times \frac{3}{3}. Multiply \frac{2-\sqrt{3}}{3} times \frac{2}{2}.

$$\frac{3\left(1+\sqrt{3}\right)}{6}+\frac{2\left(2-\sqrt{3}\right)}{6}$$

Since \frac{3\left(1+\sqrt{3}\right)}{6} and \frac{2\left(2-\sqrt{3}\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{3\left(1+\sqrt{3}\right)+2\left(2-\sqrt{3}\right)}{6}$$

Do the multiplications in 3\left(1+\sqrt{3}\right)+2\left(2-\sqrt{3}\right).

$$\frac{3+3\sqrt{3}+4-2\sqrt{3}}{6}$$

Do the calculations in 3+3\sqrt{3}+4-2\sqrt{3}.

$$\frac{7+\sqrt{3}}{6}$$

Factor

$$\frac{\sqrt{3} + 7}{6} = 1.4553418012614794$$