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# Algebra

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Find constants A and B such that
(x + 17)/(x^2 - x - 2) = A/(x - 2) + B/(x + 1)
for all x such that \$x \neq -1\$ and \$x \neq 2\$. Give your answer as the ordered pair (A,B).

Feb 12, 2022

#1
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We can use the method of partial fractions here

Note that  x^2  - x - 2   =   (x - 2)  (x + 1)

Multiply both sides by (x-2) (x + 1)   and we have this

x + 17  =  A(x + 1 ) + B ( x - 2)

1x + 17  = (A + B) x  + (A - 2B)          equate terms and we get this system of equations

A + B  =  1

A - 2B  = 17

Multiply the first equation by 2  and add to the second and we get that

3A  = 19

A = 19/3

And

A + B  = 1

19/3  + B  =1

B = 1  - 19/3  =      -16/3

Feb 12, 2022