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).
+128577 Note that x^2 - x -2 can be factored as ( X -2) ( x + 1)....multiply through by this and we get that
x - 7 = A( x + 1) + B( x - 2)
1x - 7 = (A + B)x + ( A - 2B)
Which implies that
A + B = 1 ⇒ -A - B = -1 (1)
A - 2B = - 7 (2)
Add (1) and (2) and we get that
-3B = -8
B = 8/3
And
A + 8/3 = 1
A = -5/3
(A , B) = ( -5/3, 8/3)
