Solve frac{2-frac{2sqrt{30}}{5}}{2/5}

$$\frac { 2 - \frac { 2 \sqrt { 30 } } { 5 } } { \frac { 2 } { 5 } }$$

Evaluate

$$5-\sqrt{30}\approx -0.477225575$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5}{5}.

$$\frac{\frac{2\times 5}{5}-\frac{2\sqrt{30}}{5}}{\frac{2}{5}}$$

Since \frac{2\times 5}{5} and \frac{2\sqrt{30}}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2\times 5-2\sqrt{30}}{5}}{\frac{2}{5}}$$

Do the multiplications in 2\times 5-2\sqrt{30}.

$$\frac{\frac{10-2\sqrt{30}}{5}}{\frac{2}{5}}$$

Divide \frac{10-2\sqrt{30}}{5} by \frac{2}{5} by multiplying \frac{10-2\sqrt{30}}{5} by the reciprocal of \frac{2}{5}.

$$\frac{\left(10-2\sqrt{30}\right)\times 5}{5\times 2}$$

Cancel out 5 in both numerator and denominator.

$$\frac{-2\sqrt{30}+10}{2}$$

Divide each term of -2\sqrt{30}+10 by 2 to get 5-\sqrt{30}.

$$5-\sqrt{30}$$

Factor

$$5-\sqrt{30}$$