Solve -1/sqrt{3}quad1/13-3/13

$$- \frac { 1 } { \sqrt { 3 } } \quad \frac { 1 } { 13 } - \frac { 3 } { 13 }$$

Evaluate

$$-\frac{\sqrt{3}}{39}-\frac{3}{13}\approx -0.27518079$$

Short Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\left(-\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)\times \frac{1}{13}-\frac{3}{13}$$

The square of \sqrt{3} is 3.

$$\left(-\frac{\sqrt{3}}{3}\right)\times \frac{1}{13}-\frac{3}{13}$$

Multiply -\frac{\sqrt{3}}{3} times \frac{1}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\sqrt{3}}{3\times 13}-\frac{3}{13}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\times 13 and 13 is 3\times 13. Multiply \frac{3}{13} times \frac{3}{3}.

$$\frac{-\sqrt{3}}{3\times 13}-\frac{3\times 3}{3\times 13}$$

Since \frac{-\sqrt{3}}{3\times 13} and \frac{3\times 3}{3\times 13} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\sqrt{3}-3\times 3}{3\times 13}$$

Do the multiplications in -\sqrt{3}-3\times 3.

$$\frac{-\sqrt{3}-9}{3\times 13}$$

Expand 3\times 13.

$$\frac{-\sqrt{3}-9}{39}$$

Factor

$$\frac{-\sqrt{3} - 9}{39} = -0.2751807899376635$$