Inequality Basics: You cannot multiply/divide an inequality by a variable unless you know the sign of that variable because you need to know whether or not to switch the direction of the inequality symbol. The inequality p/q > 1 does not necessarily imply that p > q (unless q is positive).
My question: if p/q = r/s. Is ps = rq?
Or here is another one:
if (x^2-y^2)/xy < 2 could it be optimised as (x-y)^2 < 2?
If YES to both my questions, then why is the rule not applicable here?
i've been known to mess up inequalities... but i would say you should be able to divide out a variable as long as it isn't zero. if you divide a variable out just take into account that you have two possibilities now; one where it is
<and> because you have to flip it if it is negative. it probably isn't useful in PS cuz maybe it leads to untrue statements, but maybe this is used in DS??
sure looks good to me.
(did you mean x-y or (x-y)^2? if you meant (x-y)^2 show me how you derived it so i can see your thought processes)