Prove an inequality

Question

Given that a>0, b>0 and c>0, prove that

(a/b + b/c + c/a) (a/c + b/a + c/b) >= 9

Answer 1

Well then each of the ratios are positive.

The common denominator inside each parenthesis is abc

THat expressions is exactly equal to:

(abc + abc + abc)/abc * (abc + abc + abc)/abc

= 3abc/(abc) * 9abc/(abc)

= 3 * 3

= 9

This shows the expressions is at least 9