$$ \frac{3-i}{2-i} + \frac{1+i}{2+i} $$

Which of the following is equal to the expression above?

(Note: \(i=\sqrt{-1}\))

Summary Submit

Use the same rules that you use with regular fraction addition:

$$ \frac{3-i}{2-i} + \frac{1+i}{2+i} $$ $$ \frac{3-i}{2-i}\cdot \left(\frac{2+i}{2+i}\right) + \frac{1+i}{2+i}\cdot \left(\frac{2-i}{2-i}\right) $$ $$ \frac{6+i-i^2}{4-i^2} + \frac{2+i-i^2}{4-i^2} $$

Substituting \(i^2=-1\):

$$\frac{7+i}{5} + \frac{3+i}{5} $$ $$ = \boxed{\frac{10+2i}{5}} $$