For a,b > 0, prove ab/(a+b) < a,b
ab / [ a + b ] < a
Since a,b > 0. multiply both sides by a + b
ab < a^2 + ab subtract ab from both sides
0 < a^2 which is true
Likewise
ab / [ a + b ] < b
ab < ab + b^2
0 < b^2
