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# Help Thanks!

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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 $$x\neq 2$$. Give your answer as the ordered pair $$(A,B)$$.

Apr 18, 2021

#1
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Cross multiply the right side to get

a(x+1)   + b (x-2)

(x^2 -x-2)                              equate the L and R numerators

a (x+1) + b(x-2) = x+7

ax + a    + bx -2b   = x + 7

from this we can get    ax + bx = x        and   a -2b = 7

a+ b =1                   a - 2b= 7         multiply red equation by -1 and add to second equation to get

-3b = 6

b = -2       then   a = 3

Apr 18, 2021
#2
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That is correct! Nice job

Guest Apr 18, 2021