Function Long division question

[tmt1]

So, I am wondering if there is a way to long divide $x+2 $ / $x -1$.

My result is $1 + \frac{4}{x -2}$ but does

$[1 + \frac{4}{x -2} ] * [ x - 2]$ = $x +2$

Thanks

 

[MarkFL]

$$\begin{array}{r}1\hspace{28px}\\x-1\enclose{longdiv}{x+2} \\ -\underline{\left(x-1\right)} \hspace{-9px} \\ 3 \end{array}$$

Hence:

$$\frac{x+2}{x-1}=1+\frac{3}{x-1}$$