Question 253151
{{{2/(3+i)}}} Start with the given expression.



{{{(2/(3+i))((3-i)/(3-i))}}} Multiply the fraction by {{{(3-i)/(3-i)}}}.



{{{(2(3-i))/((3+i)(3-i))}}} Combine the fractions.



{{{((2)(3)+(2)(-i))/((3+i)(3-i))}}} Distribute.



{{{((2)(3)+(2)(-i))/((3)(3)+(3)(-i)+(i)(3)+(i)(-i))}}} FOIL the denominator.



{{{(6-2i)/(9-3i+3i-i^2)}}} Multiply.



{{{(6-2i)/(9-3i+3i-(-1))}}} Replace {{{i^2}}} with -1.



{{{(6-2i)/(10)}}} Combine like terms.



{{{(6)/(10)+((-2)/(10))i}}} Break up the fraction.



{{{3/5-(1/5)i}}} Reduce.



So {{{2/(3+i)=3/5-(1/5)i}}}.