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 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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