ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 25 Apr 2018 05:08:26 -0500Can this fraction be simplified ?https://ask.sagemath.org/question/42157/can-this-fraction-be-simplified/During some calculations, I came across a fraction of this kind :
$$\frac{\sqrt{2}+2}{\sqrt{2}+1}$$
Which should be equal to $\sqrt{2}$.
I am surprised to see that Sage can't simplify this fraction with simplify_full :
( (sqrt(2)+2)/(sqrt(2)+1) ).simplify_full()
returns the same. Just to be sure:
bool( (sqrt(2)+2)/(sqrt(2)+1) == sqrt(2) )
returns true
Am I missing a simplification option ? How can I get Sage to simplify this fraction ?
To clarify, the original expression I encountered was this one :
$$\frac{3(x^4+4\sqrt{3}(x^2+6)\sqrt{x^2+3}+24x^2+72)}{\sqrt{3}(x^5+24x^3+72x)+12(x^3+6x)\sqrt{x^2+3}}$$
which is equal to $\frac{\sqrt{3}}{x}$. Sage can show the equality, but cannot simplify the expression (but maybe it's normal, this is not as trivial as the first example...). Substituting $x=1$ in this formula give something very similar to the expression above.
It can be obtained with:
f = 3*(x^4+4*sqrt(3)*(x^2+6)*sqrt(x^2+3)+24*x^2+72)/(sqrt(3)*(x^5+24*x^3+72*x)+12*(x^3+6*x)*sqrt(x^2+3))Florentin JaffredoWed, 25 Apr 2018 05:08:26 -0500https://ask.sagemath.org/question/42157/