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).
+129771 Note that x^2 - x - 2 can be factored as (x - 2) (x +1)
Multiply throuh by this factored form and we get
x - 7 = A(x + 1) + B( x - 2) simplify
x - 7 = Ax + A + Bx - 2B
1x - 7= (A + B)x + (A - 2B) equate coefficients and we get this system
1 = A + B
-7= A - 2B subtract the second equation from the first and we get
8 = 3B
B = 3/8
And
1 = A + 3/8
A = 5/8
(A, B) = ( 5/8, 3/8 )
