Assuming the 3 and the i are both in the denominator the
answer is
(3/2)-(i/2) or 3/2 - 1/2 i
Explanation
To simplify 5/3+i
First
multiply the numerator and the denominator by the complex conjugate of the denominator.
The complex conjugate of a denominator is 3-i. So it would look like this 5(3-i)/(3+i)(3-i)
Second
For the numerator
Distribute 5 through the parentheses and that equals 15-i. For the denominator multiply/simplify (3+i)•(3-i)=9-1^2. So the expression would look like this 15-5i/9-i^2.
Thirdly
Factor out five from the numerator: 15-5i= 5(3-i). For the denominator, 9-i^2, rewrite it as 9-(-1). (That is because i^2 by definition is equal to -1.) and 9-(-1)=9+1. So all that will look like 5(3-i)/9+1
Fourth
5(3-i)/9+1 is equal to 5(3-i)/10. After cancel out the common factor of the numerator and denominator which is 5 because 5 goes into 5 once and into 10 twice. So you’re left with the numerator being 3-i and the denominator being 2: 3-i/2.
Fifth
With 3-i/2 left, just separate the real and the imaginary parts of the expression. 3/2 - 1/2 i