# How do you simplify (3+i)/ (-2+i)?

Feb 3, 2016

$- 1 - i$

#### Explanation:

Your denominator is $- 2 + i$.

You should take the complex conjugate of the denominator $\left(- 2 - i\right)$ and expand your fraction with it:

$\frac{3 + i}{- 2 + i} = \frac{\left(3 + i\right) \cdot \textcolor{b l u e}{\left(- 2 - i\right)}}{\left(- 2 + i\right) \cdot \textcolor{b l u e}{\left(- 2 - i\right)}}$

$= \frac{- 6 - 2 i - 3 i - {i}^{2}}{{\left(- 2\right)}^{2} - {i}^{2}}$

$= \frac{- 6 - 5 i - {i}^{2}}{4 - {i}^{2}}$

... remember that ${i}^{2} = - 1$...

$= \frac{- 6 - 5 i + 1}{4 + 1}$

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

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

$= - 1 - i$