For comparison with other CAS choose from: Axiom Macsyma Maple Mathematica Reduce
(x ^2+2 sqrt(2) x+2)/(x+sqrt(2))
2
x + 2 2 x + 2
-----------------
x + 2
x + 2
sqrt(x^2-2 sqrt(2) x y+2 y^2)
2 2
(x - 2 2 x y + 2 y )
2 2 2 x - 4 y
-------------------
4