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

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SUMMARY

The maximum value of the expression 1/𝑥 + 1/𝑦, given the constraint 𝑥 + 𝑦 = 5 with 𝑥 and 𝑦 as positive integers, is achieved by evaluating all possible pairs of integers that sum to 5. The pairs (1, 4), (2, 3), (3, 2), and (4, 1) yield the values 1.25, 1.1667, 1.1667, and 1.25 respectively. Therefore, the maximum value of 1/𝑥 + 1/𝑦 is 1.25, occurring at the pairs (1, 4) and (4, 1).

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If 𝑥+𝑦=5 and 𝑥 and 𝑦 are positive integers, then the largest possible value of 1/𝑥 + 1/y is
 
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prasadini said:
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.
 
Basically, you have to do two additions of fractions.
 

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