If you find a common denominator in the two fraction you can add them without a problem
the lowest number that both 3 and 5 go into evenly is 15
you have to do the same to the top of the fraction as you do the bottom so you can rewrite this as:
5*t 3*t
----- + ------ = 1
3*5 3*5
the highlighted numbers are what we are doing to both the top and bottom of each fraction
to simplify
5t/15 + 3t/15 = 1
then add the fractions
8t/15 = 1
multiply by 15
8t=15
divide by 8
t=15/8