Note that a*b = (a^2 - b^2)/ab =(a+b)(a-b)/ab, which, when a and b are both positive, has the same sign as a - b
Given that m>n>0 1/m 0
How did Econ get mn/(m^2 - n^2)? He used the definition and simplified:
1/m * 1/n = (1/m)/(1/n) - (1/n)/(1/m) = n/m - m/n
Remember, to add or subtract fractions, you must get a common denominator - in this case mn
n/m - m/n = (n^2 - m^2)/mn
It seems that here lies his mistake