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# Algebra

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There are numbers A and B for which A/(x - 1) + B/(x + 1) = (x + 3)/(x^2 - 1) for every number x other than 1 and -1. Find .A - B.

Aug 3, 2022

#1
+2541
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We have the equation $${A \over (x - 1)} + {B \over (x + 1)} = {(x + 3) \over (x^2 - 1)}$$

Multiply by $$x^2 -1$$$$A(x+1) + B(x-1) = x + 3$$

From this, we know that $$A + B = 1$$ and $$A - B = 3$$, so $$A - B = \color{brown}\boxed{3}$$

Aug 3, 2022

#1
+2541
+1

We have the equation $${A \over (x - 1)} + {B \over (x + 1)} = {(x + 3) \over (x^2 - 1)}$$

Multiply by $$x^2 -1$$$$A(x+1) + B(x-1) = x + 3$$

From this, we know that $$A + B = 1$$ and $$A - B = 3$$, so $$A - B = \color{brown}\boxed{3}$$

BuilderBoi Aug 3, 2022