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One of the frustrations I'm always having with Sage is how it tries to "solve" inequalities. For a random example:

var('a b x')
f=(a-b*x^2)/(x-1)
solve(f>0,x)

[[x < 1, bx^2 - a > 0], [1 < x, -bx^2 + a > 0]]

Which I knew already (since it's just the numerator). Ok, so various signs and things matter, but the fact that it can't even tell me

x^2 > a/b

is frustrating. Is there a reason, or a way to convince Sage to actually "solve" these in some way?

One of the frustrations I'm always having with Sage is how it tries to "solve" inequalities. For a random example:

sage: var('a b x')
f=(a-b*x^2)/(x-1)
solve(f>0,x)

sage: f = (a - b * x^2) / (x-1) sage: solve(f > 0, x) [[x < 1, bx^2 b*x^2 - a > 0], [1 < x, -bx^2 x, -b*x^2 + a > 0]]

Which I knew already (since it's just the numerator). numerator). Ok, so various signs and things matter, but the fact that it can't even tell me

is frustrating. Is there a reason, or a way to convince Sage to actually "solve" these in some way?