I don’t think you’re cancelling the numerator, are you? I think - correct me if I’m wrong - the comparison is made by substituting in both (3t + 4r) and (rt). In fact, you can’t just cancel (3t + 4r) because the inequality flips if (3t + 4r) is negative (which is the case when r = t = -1).

Yup I am cancelling the numerator, Considered them as same & crossed it so my comparison was in between 1/rt & 1/r+t

After watching greg’s solution, i realized I am doing something wrong, Maybe a foundational concept that I have missed? Could you elaborate more on ‘Equality flips’ . No matter what we do RT>0 Right?