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).

Guest Feb 12, 2022

#1**+1 **

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

CPhill Feb 12, 2022