Question

Bài 3 ạ

Answer 1

BÀi 3:

a: \(B=\frac{2x-\sqrt{x}+2}{x-4}+\frac{1}{\sqrt{x}+2}-\frac{1}{\sqrt{x}-2}\)

\(=\frac{2x-\sqrt{x}+2+\sqrt{x}-2-\sqrt{x}-2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{2x-\sqrt{x}-2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)

b: \(B-1=\) \(\frac{2x-\sqrt{x}-2-x+4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\frac{x-\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

B<1 khi \(\frac{x-\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}<0\)

=>\(\sqrt{x}-2<0\)

=>\(\sqrt{x}<2\)

=>0<=x<4

B>1 khi \(\frac{x-\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}>0\)

=>\(\sqrt{x}-2>0\)

=>\(\sqrt{x}>2\)

=>x>4