Find constants A and B such that
(4x - 11)/(x^2 - 4x + 3) = A/(x - 1) + B/(x - 3)
for all x such that x is not equal to 1 and x is not equal to 3. Give your answer as the ordered pair (A,B).
Note that x^2 - 4x + 3 = (x -3) (x - 1) multiply through by this factor
4x - 11 = A(x - 3) + B( x - 1)
4x - 11 = (A + B) x -3A - B
Equating terms
A + B = 4 → B = 4 - A (1)
-3A - B = -11 → 3A + B = 11 (2)
Sub (1) into (2)
3A + 4 - A = 11
2A = 11 - 4
2A = 7
A = 7/2 B = 4 - 7/2 = 1/2
(A , B) = (7/2 , 1/2)