(1/(p+1)+2)/(p^2+5p+4)

Input

(1/(p + 1) + 2)/(p^2 + 5 p + 4)

Root

p = -3/2

Series expansion at p=0

3/4 - (19 p)/16 + (99 p^2)/64 - (483 p^3)/256 + (2275 p^4)/1024 + O(p^5)
(Taylor series)

Derivative

d/dp((1/(p + 1) + 2)/(p^2 + 5 p + 4)) = -(4 p^2 + 17 p + 19)/((p + 1)^3 (p + 4)^2)