\(B=\sqrt{x^2+\frac{1}{x^2}-2}-\sqrt{x^2+\frac{1}{x}+2}=\sqrt{\left(x-\frac{1}{x}\right)^2}-\sqrt{\left(x+\frac{1}{x}\right)^2}=x-\frac{1}{x}-x-\frac{1}{x}=-\frac{2}{x}\)
\(B=\sqrt{\left(x-\frac{1}{x}\right)^2}-\sqrt{\left(x+\frac{1}{x}\right)^2}=\left|x-\frac{1}{x}\right|-\left|x+\frac{1}{x}\right|=\frac{\left|x^2-1\right|}{\left|x\right|}-\frac{x^2+1}{\left|x\right|}=\frac{\left|x^2-1\right|-\left(x^2+1\right)}{\left|x\right|}\)
x2 - 1 > 0 <=> (x-1).(x+1) > 0 => x + 1 < 0 hoặc x - 1> 0 <=> x <-1 hoặc x > 1
Vậy
+) Khi x < -1 => B = \(\frac{x^2-1-\left(x^2+1\right)}{-x}=\frac{2}{x}\)
+) Khi -1< x< 0 thì B = \(\frac{-\left(x^2-1\right)-\left(x^2+1\right)}{-x}=\frac{-2x^2}{-x}=2x\)
+) Khi 0 < x < 1 thì B = \(\frac{-\left(x^2-1\right)-\left(x^2+1\right)}{x}=\frac{-2x^2}{x}=-2x\)
+) Khi x > 1 thì B = \(\frac{\left(x^2-1\right)-\left(x^2+1\right)}{x}=\frac{-2}{x}\)
