MHB Partial Fraction Simplification

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To simplify the partial fraction expression, the multiplication of the binomials (Bx + C)(x + 3) needs to be performed. This results in Bx^2 + (3B + C)x + 3C. When combined with the other term (x^2 + 9), the overall expression becomes (B + 1)x^2 + (3B + C)x + (9 + 3C). This matches the textbook's formulation, confirming the derivation process. Understanding this multiplication is crucial for mastering partial fraction decomposition.
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I have this partial fraction:

$$ 18 = (x^2 + 9) + (Bx + C)(x + 3)$$

which the textbook says is equal to:

$$(B + 1)x^2 + (C + 3B)x + (9 + 3C)$$

But I don't follow this step. How do I derive this?
 
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Okay, we begin with:

$$\left(x^2+9\right)+(Bx+C)(x+3)$$

What to you get when you carry out the indicated multiplication of the two binomial expressions?
 

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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