# How do you simplify 5/(2-i)?

Aug 7, 2018

$2 + i$

#### Explanation:

$\frac{5}{2 - i}$

Multiply numerator and denominator by the denominator's conjugate:
$= \frac{5}{2 - i} \textcolor{b l u e}{\cdot \frac{2 + i}{2 + i}}$

Simplify:
$= \frac{10 + 5 i}{4 - {i}^{2}}$

$= \frac{10 + 5 i}{4 + 1}$

$= \frac{10 + 5 i}{5}$

$= 2 + i$