Find constants a and b such that (2x + 17)/(x^2 - x - 2) = a/(x - 2) + b/(x + 1) for all x such that x≠-1 and x≠2.
+129850 X^2 - x - 2 = (x -2) ( x + 1)
Multiply through by ( x -2) ( x + 1) and we have that
2x + 17 = a( x + 1) + b ( x + 2)
2x + 17 = (a + b)x + (a + 2b) which implies that
a + b = 2 ⇒ - a - b = -2 (1)
a + 2b = 17 (2)
Add (1) and (2)
b = 15
a + b = 2 ⇒ a + 15 = 2 ⇒ a = 2 -15 ⇒ a = -13
