Maple: command to simplify fraction

Question

Why doesn't Maple simplify a fraction like

-sqrt(5)*(5+sqrt(5))/120

to (-1-sqrt(5))/24 ?

Are there any commands to do this?

Answer 1

A suitable command for this is radnormal.

ee:=-sqrt(5)*(5+sqrt(5))/120;

                            1   (1/2) /     (1/2)\
                   ee := - --- 5      \5 + 5     /
                           120                    

radnormal( ee );

                            1    1   (1/2)
                          - -- - -- 5     
                            24   24       

There are a few others which can get the form (at least for this particular example).

expand( ee );

                            1    1   (1/2)
                          - -- - -- 5     
                            24   24       

evala(Normal( ee ));

                            1    1   (1/2)
                          - -- - -- 5     
                            24   24       

Note that the distribution of the factor 1/24 is done here by Maple as an automatic simplification (and which is usually difficult to disable or awkward to avoid). Notice how delayed evaluation won't prevent it.

'(-1-sqrt(5))/24';
                            1    1         
                          - -- - -- sqrt(5)
                            24   24