How to solve this step by step?
Thank you guys so much that helped me alot :D
Paste that in Wolfram|Alpha and click step-by-step link. Here is what you get:
Sometimes you can see it directly with commands such as simplify/factor/apart
Now it is easy to see the value when x "approaches" 3 :)
What do you mean when you say "Step by Step"? It's just
Limit[(x^3 - 13 x^2 + 51 x - 63)/(x^3 - 4 x^2 - 3 x + 18), x -> 3]
(* Out= -(4/5) *)
If you like a mathematical explanation, you should consider asking this on math.stackexchange.com
What i ment by "step by step" is how did you evaluate the limit to end up with this answer
If you have Mathematica of a sufficiently recent version installed then you can open an empty notebook and type
=Limit[(x^3 - 13 x^2 + 51 x - 63)/(x^3 - 4 x^2 - 3 x + 18), x -> 3]
and shift and enter to evaluate that. That leading "=" tells Mathematica to send the question off to WolframAlpha.com, get the result and then display it.
That comes back with -4/5
But there should be a little grey "+" in the upper right corner of that and if you click on that + it will give you more details. Part of those details is SOMETIMES a button button labelled "Step-by-step solution" and if you click on that then SOMETIMES you get a fairly detailed description of the steps taken to find that -4/5. In this case it isn't too bad. But for some problems there is no set of steps available, because the methods used just don't translate into anything you could use.
You can get similar information with a paid subscription to WolframAlpha.com but I myself have never seen a compelling enough clear enough description of all the additional features, other than getting to see some steps, I would get from subscribing and thus have not tried that. Your preference may differ.