Melody

\(\displaystyle \lim_{x\rightarrow 0} \;\frac{x}{tanx} =1\)

I think this is one of those things that you are meant to memorize. 

\(\frac{2x^2 - 3x}{(x^2 - x) }+ 5x - 11 =\frac{ (3x^2 + 4)}{(x^2 - 1)}\)

Start by factorizing the numerators and the denominators of the fractions.

Cancel out common factors

Then get back to us with what you have.

What is the sine rato? 

(Your turn to ansswer)

That is not the right answer.

I used the euclidean algorithm to solve this :

How about proofreading your question.  It is nonsense.

The first ball can go in any of the 3 boxes, that is 3 ways

the second ball can go int any of the 3 boxes that together with the first ball is 3*3=3^2=9 way

so for 6 balls it would be  3^6 ways.

Why don't you tell us your thoughts first?

Thanks for providing us with the solution abc ...

I am sure a number of us will examine it   

Here is Alan's answer graphed, from Desmos.

I wouldn't guess that this was a degree 5 polynomial.  (without doing lots of work)  

Although it would have to be an odd degree.  That makes 5 reasonable I guess.