Question

x/(x^3-1)(x+2) resolve into partial fraction​

Answer 1

Answer:

 = 1/9(x-1 ) + (-x/3 +1/6)/(x²+x +1 ) - 1/9(x+2)

Step-by-step explanation:

x/(x^3-1)(x+2) = P

P = x/(x^3-1)(x+2)

  =  x/(x-1)( x²+x+1)(x+2)

  = A/(x-1 ) + (Bx +C)/(x²+x +1 )+ D/(x+2)

x = A( x²+x+1)(x+2) + (Bx +C)(x-1)(x+2) + D(x-1)( x²+x+1)

at x = 1 ,  1 = 9A  , A = 1/9

at x = -2 , -2 = -9D, D = - 1/9

at x = 0 ,  0 = 2A -2C - D , 2C = 2A - D , 2C= 3/9 , C = 1/6

at x = 2 , 2 = 28A + 4( 2B +C) + 7D , 4( 2B +C) = 2 - 28A - 7D = 2 - 28/9 + 7/9

4( 2B +C) = 25/9 - 28/9 = - 3/9

P = A/(x-1 ) + (Bx +C)/(x²+x +1 )+ D/(x+2)

  = 1/9(x-1 ) + (-x/3 +1/6)/(x²+x +1 ) - 1/9(x+2)