Question

$\frac{1}{2+ \sqrt{5} } + \frac{1}{2- \sqrt{5} }$

Answer 1

rationalizam numitorii, primul cu 2-√5, al doilea cu 2+√5
(2-√5)/(4-5)+(2+√5)/(4-5)=
-2+√5-2-√5=-4

Answer 2

$\frac{1}{2+\sqrt5}+\frac{1}{2-\sqrt5}=\frac{2-\sqrt5\;+\;2+\sqrt5}{4-5}=\frac{4}{-1}=\;-\,4$

Obs.  numitorul comun=c.m.m.m.c.=[2+√5 ; 2-√5] = (2+√5)(2-√5) !