Question

solve: (x2 - 10x + 13)/((x + 1)(x2 - 5x + 6))

Answer 1

Let

x2 – 10x + 13 = A(x - 2)(x – 3) + B(x +1) (x – 3) + C(x + 1) (x – 2)

Put x=-1, 1 + 10 + 13 = A (-3) (-4) + 0 + 0

24 = 12A ⇒ A = 24/12 = 2

Put x = 2, 4 – 20 + 13 A(0) + B(3) (-1) + C(0) -3

= -3B ⇒ B = 1

Put x = 3, 9 – 30 + 13

= A(0) + B(0) + C(4) (1) -8 = 47 ⇒ C= -2