1. Simplifying rational functions

I know i should be able to do this but I've got a mind block at the moment.
$\frac{x+5+\frac{4}{x}}{x+3+\frac{-4}{x}}$
i KNOW this rationalizes down to $\frac{x+1}{x-1}$ because that's the answer, but i can't for the life of me figure out why this is the case, i keep getting $\frac{x+9}{x-1}$
any help would be appreciated

2. $

\frac{x+5+\frac{4}{x}}{x+5+\frac{-4}{x}}
$

$\frac{x^2+5x+4}{x^2+5x-4}$

I don't think that goes into $\frac{x+1}{x-1}$. Have you written down the question correctly?

3. indeed i did not, thanks for pointing that out, the proper question is in the original post now

4. Ahh!

That's a bit better:

$

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

5. i knew it was something simple, haven't used my factorizing skills in far too long lol
thanks