Answer
$\frac{14}{25}-\frac{2}{25}i$.
Work Step by Step
The given expression is
$=\frac{4}{(2+i)(3-i)}$
Use the FOIL method.
$=\frac{4}{6-2i+3i-i^2}$
Use $i^2=-1$.
$=\frac{4}{6-2i+3i+1}$
Add like terms.
$=\frac{4}{7+i}$
The conjugate of the denominator is $7-i$.
Multiply the numerator and the denominator by $7-i$.
$=\frac{4}{7+i}\cdot \frac{7-i}{7-i}$
Use the special formula $(A+B)^2=A^2+2AB+B^2$
$=\frac{28-4i}{7^2-i^2}$
Use $i^2=-1$.
$=\frac{28-4i}{49+1}$
Simplify.
$=\frac{28-4i}{50}$
Rewrite as $a+ib$.
$=\frac{28}{50}-\frac{4}{50}i$
Simplify.
$=\frac{14}{25}-\frac{2}{25}i$.
