2
-----
 3+i

Multiply by the conjugate of the bottom, which is formed by
changing the sign of the term with "i" (leaving the sign of
the term without the "i").

The conjugate of 3+i is 3-i.  So we put that over itself 
so it will equal 1 and therefore not change the numerical value of the
given expression:

  2      3-i 
----- × -----
 3+i     3-i

Then multiply out the top and bottom, distributing on top and
using FOIL on the bottom:

    6-2i       
------------ 
 9-3i+3i-i²

Cancel the two middle terms on the bottom:

  6-2i       
------- 
  9-i²

Replace i² by (-1)


   6-2i       
 -------- 
  9-(-1)

   6-2i       
 -------- 
   9+1

   6-2i       
 -------- 
    10

Factor 2 out of the top:

  2(3-i)       
 -------- 
    10

Cancel the 2 into the 10 getting 5

 3-i
 ---
  5

Make two fractions:

 3     i
--- - ---
 5     5

But you can write the last term as one-fifth of i
since dividing by 5 is the same as multiplying by 

Answer:  

Edwin