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Question 14

The fraction $$\frac{B}{3x-1}$$ is subtracted from the fraction $$\frac{A}{2x+3}$$. The resulting fraction is $$\frac{-11}{(2x+3)(3x-1)}$$. Then $$A+B=$$

Solution

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Subtracting gives $$\frac{A(3x-1)-B(2x+3)}{(2x+3)(3x-1)}=\frac{-11}{(2x+3)(3x-1)}$$, so $$A(3x-1)-B(2x+3)=-11$$ for all $$x$$. Matching the $$x$$ coefficient gives $$3A=2B$$, and matching constants gives $$-A-3B=-11$$, which together give $$B=3$$, $$A=2$$, so $$A+B=5$$.

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