УНСС

[Гост]

Как трябва да се преобразува този израз ?

[Добромир Глухаров]

$a>1\Rightarrow|a|=a;|a+1|=a+1;|a-1|=a-1\Rightarrow$

$\Rightarrow\sqrt{a^2}=a;\sqrt{(a+1)^2}=a+1;\sqrt{(a-1)^2}=\sqrt{(1-a)^2}=a-1$

$\sqrt{\frac{1}{a^2}+\frac{2}{a}+1}-\sqrt{\frac{1}{a^2}-\frac{2}{a}+1}=\sqrt{\frac{1+2a+a^2}{a^2}}-\sqrt{\frac{1-2a+a^2}{a^2}}=$

$=\frac{\sqrt{(1+a)^2}-\sqrt{(1-a)^2}}{a}=\frac{1+a-(a-1)}{a}=\frac{2}{a}$