+1222 Let a and b be positive real numbers such that a + b = 1. Find the set of all possible values of a/b.
+1910 First off, we need to put a in terms of b. This helps us identify a range.
We get
\(a+b=1\\ a=1-b\)
Now, plugging that into the expression, we get
\(\frac{1}{a}+\frac{1}{b}= \frac{1}{1-b}+\frac{1}{b}=\frac{b+1-b}{b-b^2}=\frac{1}{b-b^2}\)
Now, we can easily find the set of all real numbers. We have
\(\{ R>1\} |\{a,b\} \subset R\) where \(1> a,b > 0\)
Thanks! :)
