Answer:
1 - y + y²
Step-by-step explanation:
1 + y³ is a sum of cubes and factors in general as
a³ + b³ = (a + b)(a² - ab + b²) , then
1 + y³
= (1 + y)(1² - 1(y) + y²) = (1 + y)(1 - y + y²)
Then
[tex]\frac{1+y^3}{1+y}[/tex]
= [tex]\frac{(1+y)(1-y+y^2)}{1+y}[/tex] ← cancel out the common factor (1 + y)
= 1 - y + y²
