Solve -1/2left(-frac{8sqrt{5}}{5}-4right)-2

$$- \frac{ 1 }{ 2 } \left( - \frac{ 8 \sqrt{ 5 } }{ 5 } -4 \right) -2$$

Evaluate

$$\frac{4\sqrt{5}}{5}\approx 1.788854382$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{5}{5}.

$$-\frac{1}{2}\left(-\frac{8\sqrt{5}}{5}-\frac{4\times 5}{5}\right)-2$$

Since -\frac{8\sqrt{5}}{5} and \frac{4\times 5}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}\times \frac{-8\sqrt{5}-4\times 5}{5}-2$$

Do the multiplications in -8\sqrt{5}-4\times 5.

$$-\frac{1}{2}\times \frac{-8\sqrt{5}-20}{5}-2$$

Multiply -\frac{1}{2} times \frac{-8\sqrt{5}-20}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(-8\sqrt{5}-20\right)}{2\times 5}-2$$

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

$$\frac{-\left(-8\sqrt{5}-20\right)}{2\times 5}-\frac{2\times 2\times 5}{2\times 5}$$

Since \frac{-\left(-8\sqrt{5}-20\right)}{2\times 5} and \frac{2\times 2\times 5}{2\times 5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\left(-8\sqrt{5}-20\right)-2\times 2\times 5}{2\times 5}$$

Do the multiplications in -\left(-8\sqrt{5}-20\right)-2\times 2\times 5.

$$\frac{8\sqrt{5}+20-20}{2\times 5}$$

Do the calculations in 8\sqrt{5}+20-20.

$$\frac{8\sqrt{5}}{2\times 5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{4\sqrt{5}}{5}$$