MHB What is the Maximum Value of 1/𝑥 + 1/𝑦 with x+y=5 and Positive Integers?

[prasadini]

If 𝑥+𝑦=5 and 𝑥 and 𝑦 are positive integers, then the largest possible value of 1/𝑥 + 1/y is

 

[Opalg]

If 𝑥+𝑦=5 and 𝑥 and 𝑦 are positive integers, then the largest possible value of 1/𝑥 + 1/y is

There are not many ways of expressing 5 as the sum of two positive integers. I suggest that you look at each of them in turn, and find which one gives the best result for 1/𝑥 + 1/y.

 

[HallsofIvy]

Basically, you have to do two additions of fractions.