Question

Tentukan nilai p dan q jika 3x+4/x²-x-2 = p/x-2+q/x+1

Answer 1

Verified answer

(3x + 4)/(x² - x - 2) = p/(x - 2) + q/(x + 1)
(3x + 4)/(x - 2)(x + 1) = (p(x + 1) + q(x - 2))/(x - 2)(x + 1)

Perhatikan pembilangnya
3x + 4 = p(x + 1) + q(x - 2)
3x + 4 = (p + q)x + (p - 2q)

3x = (p + q)x
p + q = 3 ... (1)

p - 2q = 4 ... (2)

(1) - (2)
3 - 4 = q - (-2q)
-1 = 3q
q = -1/3

p = 3 - q = 10/3