Isolating variable confounded by cursed reciprocals

lundi 28 avril 2014

1. The problem statement, all variables and given/known data



Given



1) xy = 1



2) x(t^2)-y = (t^3)-1/t



Express x in t, y in t







2. The attempt at a solution





x/t = [(tx+1)(td-1)] / [(t^2)-1] but I still can't separate t and x, driving me mad it is.



Also subtracted 1) from 2) to obtain



(t^2)x - (t^3) +1/t -1/x = 0



but no progress from there.





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