Yes, 0 must be removed of roots sets.
when you ask for support, please post all content of sage cell, like this :
solve([(4*x+5)/(x^2)>=4/(x+5)],x)
There are many posts like yours (for quadratic equations ...) but the
current status is wrong (or no result) computations for "special" symbolic
expressions, even if you try to force the domain of roots like, x =
var('x',domain="real")
It's because some limits of the simplifying symbolic code .. even some
formula like sqrt(x^4) is not simplified to x^2 (try: f(x) = sqrt(x^4) ;
print "f : ",f.factor() ... or expand() or simplify()
I always "help" the software simplifying,....usually writting in polynomial
form and then factor.
It can be very painful, especially for mathematics where quadratic
equations or inequations appear like in cartesian coordinates plane
geometry.
Dominique
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