Answer:
2(y^2 +4y+2)
----------------------------
(y+1)^2(y+2)
Step-by-step explanation:
2y 4
--------------- + -------------
y^2 +2y+1 y^2 +3y+2
Factor the denominators
2y 4
--------------- + -------------
(y+1)(y+1) (y+2)(y+1)
Get a common denominator
2y (y+2) 4(y+1)
--------------- + -------------
(y+1)^2(y+2) (y+2)(y+1)^2
Distribute in the numerator
2y^2+4y 4y+4
--------------- + -------------
(y+1)^2(y+2) (y+2)(y+1)^2
Combine like terms
2y^2 +8y+4
----------------------------
(y+1)^2(y+2)
Factor out a 2
2(y^2 +4y+2)
----------------------------
(y+1)^2(y+2)
