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

Dec 18, 2015

$\frac{7}{10} + \frac{1}{10} i$

#### Explanation:

Multiply by the complex conjugate of the denominator.

$\frac{2 + i}{3 + i} \left(\frac{3 - i}{3 - i}\right) = \frac{6 + i - {i}^{2}}{9 - {i}^{2}}$

Recall that since i=sqrt(-1),color(red)(i^2=-1.

$= \frac{6 + i - \left(- 1\right)}{9 - \left(- 1\right)} = \frac{7 + i}{10} = \frac{7}{10} + \frac{1}{10} i$