# [Maxima] How to simplify ((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3))) + (2-sqrt(3))/(sqrt(2)-sqrt(2-sqrt(3))))^2 to 2?

Nicolas Pettiaux nicolas.pettiaux
Tue Nov 14 15:25:36 CST 2006

```2006/11/14, Andrej Vodopivec <andrej.vodopivec at gmail.com>:
> On 11/14/06, Humberto Bortolossi <humberto.bortolossi at gmail.com> wrote:
> > Hi!
> >
> > Is there a way to make Maxima simplify the expression
> >
> > ((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3))) +
> > (2-sqrt(3))/(sqrt(2)-sqrt(2-sqrt(3))))^2
> >
> > to 2?
>
> (%i2) ((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3))) +
> (2-sqrt(3))/(sqrt(2)-sqrt(2-sqrt(3))))^2\$
> (%i3) ratsimp(scanmap(sqrtdenest, ratsimp(%)));
> (%o3) 2

thanks.

Now we know maxima can do it ... but the user have to deal with

1/ know to load that precise module. How can they find it ?
2/ know how to ask maxima to use it as the expression
> (%i3) ratsimp(scanmap(sqrtdenest, ratsimp(%)));
does not appear as a simple one to me.

How could I (and my student) have come to this ?

Thanks,

Nicolas
--
Nicolas Pettiaux - email: nicolas.pettiaux at ael.be

```