How do you simplify (1/2 + 2/(5i)) + (1/20 - 1/(5i))?

Jul 17, 2015

$\frac{11}{20} + \frac{1}{5 i}$

Explanation:

$\left(\frac{1}{2} + \frac{2}{5 i}\right) + \left(\frac{1}{20} - \frac{1}{5 i}\right)$

We can remove the parenthesis:

$\frac{1}{2} + \frac{2}{5 i} + \frac{1}{20} - \frac{1}{5 i}$

Rearranging a bit:

$\frac{1}{2} + \frac{1}{20} + \frac{2}{5 i} - \frac{1}{5 i}$

We need to make the denominators of $\frac{1}{2}$ and $\frac{1}{20}$ alike and we can see that the denominators of $\frac{2}{5 i}$ and $- \frac{1}{5 i}$ are already alike.

$\frac{1}{2} \cdot \frac{10}{10} = \frac{10}{20}$

So,

$\frac{1}{2} + \frac{1}{20} + \frac{2}{5 i} - \frac{1}{5 i} = \frac{10}{20} + \frac{1}{20} + \frac{2 - 1}{5 i}$

$= \frac{11}{20} + \frac{1}{5 i}$