Let \(a\) and \(b\) be positive real numbers such that \(a + b = 1.\) Find set of all possible values of \(\frac{1}{a} + \frac{1}{b}.\)

\(b=1-a\\ \dfrac 1 a + \dfrac 1 b = \\ \dfrac 1 a + \dfrac{1}{1-a} = \\ \dfrac{1-a+a}{a(1-a)} = \\ \dfrac{1}{a(1-a)} \in (-\infty,0) \cup [4,\infty)\)

The sum has to be positive

duh, right you are.

it's just \([4, \infty)\)

It is good to see that our answers are getting looked at

Thanks Rom and guest.