Help with limits to infinity

I'm in a beginning calculus class after not touching math of any sort for 4 years. I've forgotten a lot of the more complicated algebra, and I'm struggling with simplifying limits right now. I'm doing my homework right now and coming across a lot of problems I'm getting wrong and I can't understand why, so I am asking for help.

first problem:

1.)

To work this one out, I multiplied the top and bottom by ,

so I get

From there, I divided everything by since that's the highest x value in the denominator in order to get rid of some of the numbers. I wind up with:

Which is which equals

The back of my book however says this answer should just be 3. Why is the x^3 cancelled?

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Here's another I got wrong:

All I could think to do was to divide everything by X but I don't even think you're allowed to do that without a denominator (are you?). Anyway when I do that I get

Apparently the answer is supposed to be 1/6, how do you get this?