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This is my first post so please be gentle with me!

Limit of this rational function as x approaches infinity?

f(x) = (x^3 - 2x)/(2x^2 - 10)

I was under the impression that if the degree of the polynomial of the numerator exceed that of the denominator then there could be no horizontal asymptote. Is this correct?

I've used l'hopitals rule and found the limit to be 3x/2. I've been told the limit as x tends to infinity is x/2. Which is the correct solution and why? This has been driving me crazy!!

Damian