Inequality problem

Question

3<a<4 and 4<b<5 find b/3a-a/3b

Answer 1

(b/3a)-(a/3b)=(b²-a²)/3ab

maximum numerator/denominator is (25-9)/(3*5*3)=16/45

minimum numerator is zero

range of (b/3a)-(a/3b) is (0,16/45)