Question

Find values of x for which the following is positive

x / (x^2 + 4)

Logically, x / (x^2 + 4) > 0 and thus, x > 0 because if x is <= 0, that would mean that the whole expression will be <= 0, but I'm not sure if this is the exact same way that this problem should be solved in. So am I on the right track? Like should I do this in some sort of mathematical steps? Thank you!

Answer 1

you should post this in Mathematics, not Calculus.
But your analysis is correct.
More generally, if you had f(x)/g(x) >0
this would require either (1) both f(x)>0 and g(x)>0 or (2) both f(x)<0 and g(x) < 0 (negative divided by negative is positive)

in your problem g(x) >0 which leaves you only with case (1): f(x)>0 i.e. x >0

Answer 2

Yeah, sorry for being off-topic, but this is actually from Calculus with Analytic Geometry (first chapter) and that's why I thought about posting here. Thanks anyway!