Jazmin Perry

2022-02-01

How do you simplify $\frac{5-i}{3+3i}?$

### Answer & Explanation

ocretz56

Step 1
You must use something that resembles rationalization with roots at the denominator: multiply both numerator and denominator by $3-3i$
$\frac{5-i}{3+3i}×\frac{3-3i}{3-3i}=\frac{\left(5-i\right)\left(3-3i\right)}{\left(3+3i\right)\left(3-3i\right)}$
and use the fact that
$\left(3+3i\right)\left(3-3i\right)={3}^{2}-{\left(3i\right)}^{2}=9-9{i}^{2}=9+9=18$
Then, expand the numerator as usual:
$\left(5-i\right)\left(3-3i\right)$
$=15-15i-3i+3{i}^{2}$
$=15-18i-3$
$12-18i$
We can simplify something:
$\frac{12-18i}{18}=\frac{2}{3}-i$

Do you have a similar question?

Recalculate according to your conditions!