Without calculus

Given that u>0 and v>0 find the smallest possible value of 1/u + 1/v given that u + v = 5 by different methods.
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Problem



Given that $u> 0$ and $v> 0$ what is the smallest possible value of $1/u + 1/v$ given that $u + v = 5$?

Can you find this value by more than one method (not involving trial and error) without using calculus?