Maths唔識抵死題

6 /( x^4 - 5x^2 + 4)
= 6 / (x^2 -4) (x^2 -1)
= 6 / ( x+2) (x-2) (x+1) (x-1)--------(1)
Let this be A/(x+2) + B/(x-2) + C/(x+1) + D/(x-1)
thus 6 / ( x+2) (x-2) (x+1) (x-1) = A/(x+2) + B/(x-2) + C/(x+1) + D/(x-1)
6 = A (x-2)(x+1)(x-1) + B (x+2)(x+1)(x-1) + C (x+2)(x-2)(x-1) + D (X+2)(x-2)(x+1)
When x = -2,
6 = A (-4)(-1)(-3)
A = -1/2
When x = 2,
6 = B (4)(3)(1)
B = 1/2
When x = -1,
6 = C (1)(-3)(-2)
C=1
When x = 1,
6 = D (3)(-1)(2)
D = -1

therefore,
6 / x^4 - 5x^2 + 4
= -1/2(x+2) + 1/2(x-2) + 1/(x+1) - 1/(x-1)