We are given, for a,b>0

$\displaystyle f(a,b)=\frac{a-b}{ln a-ln b} \ \ \ if a \neq b$

and

$\displaystyle f(a,b)=a $ if a=b

prove that f(a,b) is strictly increasing in both a and b

I take the derivative, but I can't prove that it is positive. Help is much appreciated