Find constants A and B such that
(x + 7)/(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).
+130511 This is a partial fractions problem....note that x^2 - 4x + 3 = (x - 3) ( x -1)
So we have
(x + 7) A B
___________ = _____ + ______ multiply through by ( x -3) (x -1)
(x -3) ( x -1) x -1 x - 3
We have
x + 7 = A(x -3) + B(x -1)
x + 7 = Ax - 3A + Bx - B
1x + 7 = ( A + B)x -3A -B
Equating terms gives us this system
A + B =1
-3A - B = 7 add these
-2A = 8
A = -4
And
-4 + B = 1
B = 5
(A,B) = (-4, 5)
