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).
+130068 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
