Find A and B such that (4x + 18)/(x^2 - 8x + 15) = A/(x - 3) + B/(x - 5) for all x besides 3 and 5. Express your answer as an ordered pair in the form (A,B).
+128460 Method of Partial Fractions :
Note that (x^2 - 8x + 15) = ( x -3) (x - 5)
Mutiply the equation by this and we get that
4x + 18 = A(x - 5) + B ( x - 3)
4x + 18 = (A + B)x - ( 5A + 3B) equate coefficients and constants
A + B = 4 ⇒ B = 4 - A (1)
-5A - 3B = 18 (2)
Sub (1) into (2)
-5A - 3(4 - A) = 18
-5A - 12 + 3A = 18
-2A - 12 = 18
-2A = 30
A = -15
B = 4 - -15 = 19
(A,B) = ( -15, 19)
