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0
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+105

Find constants A and B such that

$$\frac{x - 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}$$

for all x such that $$x \neq 1$$ and $$x \neq 2$$.

Aug 15, 2021

#1
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Letting x go to 2, we find that A + 2B = 4.  Letting x go to -1, we find 2A - B = 3.  Therefore, A = 2 and B = -1.

Aug 15, 2021
#2
+105
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x does not equal 1 or 2 though. I am confused. Can you explain?

QuestionableBean  Aug 15, 2021
#3
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If you let x go infinity, then you get 0 = A + B.

If you let x = 0, then you get 7/2 = A/(-2) + B.

The solution to this system is then A = -7/3, B = 7/3, so (A,B) = (-7/3,7/3).

Aug 15, 2021