1956 AHSME Problems/Problem 17

This is essentially asking for the partial fraction decomposition of $\frac{5x-11}{2x^2 + x - 6}$ Looking at $A$ and $B$ , we can write $$ (Error compiling LaTeX. Unknown error_msg)A(2x-3) + B(x+2) = 5x-11 $. Substituting$ x= -2 $, we get <cmath>A(-4-3) + B(0) = -21 \Rrightarrow A = 3</cmath> Substituting$ x = \frac{3}{2} $, we get <cmath>A(0) + B(\frac{7}{2}) = \frac{15}{2} - \frac{22}{2} \Rrightarrow B = -1</cmath> Thus, our answer is$ \boxed{D}$

~JustinLee2017

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1956 AHSME Problems/Problem 17