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Let $A$ and $B$ be real numbers such that $\frac{A}{x-5}+B(x+1)=\frac{-3x^2+12x+22}{x-5}$. What is $A+B$?

 Aug 29, 2021
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By long division, (-3x^2 + 12x + 22)/(x - 5) = -4x -4 + 9/(x - 5) = 9/(x - 5) + (-4)(x + 1), so A + B = 9 + (-4) = 5.

 Aug 29, 2021

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