MHB Function Long division question

AI Thread Summary
The discussion revolves around performing long division on the expression (x + 2) / (x - 1). The initial result presented is 1 + 4/(x - 2), but there is confusion regarding its correctness. The correct long division yields 1 + 3/(x - 1) instead. The participants clarify that multiplying the derived expression by (x - 2) does not return to the original expression. The final conclusion confirms that the accurate division result is indeed 1 + 3/(x - 1).
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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
 
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$$\begin{array}{r}1\hspace{28px}\\x-1\enclose{longdiv}{x+2} \\ -\underline{\left(x-1\right)} \hspace{-9px} \\ 3 \end{array}$$

Hence:

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