Division Algorithm y^3 +3y +4 / y+1?

Wiki article: http://en.wikipedia.org/wiki/Polynomial_long_divis...

My solution: http://img60.imageshack.us/img60/8773/21581159ol8....

Answer: y^2 - y + 4

Synthetically divide the numerator by -1 to get y^2 - y + 4

Rewrite the fraction, replacing the numerator with the product of the quotient and the divisor of the synthetic division:

[(y+1)(y^2 - y +4)] / (y+1)

The (y+1) cancel in the numerator and denominator to get:

y^2 - y + 4

y^3 +3y +4 = y^2(y+1)-y(y+1)+4(y+4)

So,

y^3 +3y +4 / y+1 = y^2 - y + 4

is that

y³ +3y + (4/y) +1

or

y³ +3y + (4/(y +1))

or

(y³ +3y + 4) / (y +1)

or

etc

??