Maxima 5.9.1 vs MuPAD 2.5.3



To simplify (2+sqrt(5))/(4+3*sqrt(5)) --> (2*sqrt(5)+7)/29, use
ratsimp with algebraic set to true.

(%i1) e : (2+sqrt(5))/(4+3*sqrt(5))$
(%i2) algebraic : true$
(%i3) ratsimp(e);
(%o3) (2*sqrt(5)+7)/29
(%i4) algebraic : false$
(%i5) ratsimp(e);
(%o5) (sqrt(5)+2)/(3*sqrt(5)+4)

Barton