Answer:
(1/3) / (x+1) + (-1/3) / (x+4)
Step-by-step explanation:
1 / (x+1)(x+4) = (A/x+1) + (B/x+4)
1 = ((A/x+1) + (B/x+4)) * (x+1)(x+4)
1 = A*(x+4) + B*(x+1)
* if x = -4
1 = A*(-4+4) + B*(-4+1)
1 = B*(-3)
B = -1/3
** if x = -1
1 = A*(-1+4) + B*(-1+1)
1 = A*(3)
A = 1/3
check: (1/3)/(x+1) + (-1/3)/(x+4) = ((1/3)*(x+4))/((x+1)(x+4)) + ((-1/3)*(x+1))/((x+1)(x+4))
==> ((1/3x + 4/3)+(-1/3x - 1/3)) / ((x+1)(x+4)) = 1 / (x+1)(x+4)
