Brody added a fraction to 5/6 to get 31/30. use the equation a/b + c/d = (ad +bc)/ bd to find the fraction he added

The fraction he added is 6/30, or 1/5.
I'm not 100% sure about the equation you want me to use but I did the work this way:

5/6+x/30=31/30 (the denominator has to equal 30 because you are adding. You need a common denominator which is why you need to change 5/6. We can label the numerator as a hidden value x)

25/30+x=31/30

You can then work backwards and basically subtract 25 from 31 and get 6; so x=6