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sage: f(x)=(4*3+3*x)/(-12+2*x)
sage: f.limit(x=Infinity)
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or

sage: g=(4*3+3*x)/(-12+2*x)
sage: g.limit(x=Infinity)
3/2

or with $f$ and $g$ defined as above,

sage: limit(f, x=Infinity)
3/2
sage: limit(f(x), x=Infinity)
3/2
sage: limit(g, x=Infinity)
3/2

You can also leave out the asterisks:

sage: implicit_multiplication(True)
sage: g=(12+3x)/(-12+2x)