first multiply the top and bottom by the opposite operation by "FOIL-ing"
notice it was *3 - i* but you multiply *3 + i*
[tex] \frac{2 + i}{3 - i} \times \frac{3 + i}{3 + i} = \frac{6 + 3i + 2i + {i}^{2} }{10 } = \frac{5 + 5i}{10} [/tex]
then simplify:
TOP:
--------
(i² = -1)
6 + i²
6 + -1 = 5
3i + 2i = 5i
BOTTOM:
--------------
3 • 3 = 9
-i • i = 1
9 + (1) = 10
