Amplifici prima fractie cu 1-¬/2
A doua cu ¬/2-¬/3
Si a triea cu ¬/3-¬/4
[tex]=\frac{1-\sqrt{2}}{1-2}+\frac{\sqrt{2}-\sqrt{3}}{2-3}+\frac{\sqrt{3}-\sqrt{4}}{3-4}=[/tex]
[tex]=-(1-\sqrt{2})-(\sqrt{2}-\sqrt{3})-(\sqrt{3}-\sqrt{4})=[/tex]
[tex]=-1+\sqrt{2}-\sqrt{2}+\sqrt{3}-\sqrt{3}+\sqrt{4}=[/tex]
[tex]=-1+\sqrt{4}=[/tex]
[tex]=-1+2=[/tex]
[tex]\boxed{=1}[/tex]
