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