MHB Function Long division question

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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:

$$\frac{x+2}{x-1}=1+\frac{3}{x-1}$$
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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