a, Với x >= 0 ; x khác 9
\(B=\dfrac{2\sqrt{x}\left(\sqrt{x}-3\right)+\sqrt{x}\left(\sqrt{x}+3\right)-3x-3}{x-9}=\dfrac{2x-6\sqrt{x}+x+3\sqrt{x}-3x-3}{x-9}=\dfrac{-3\sqrt{x}-3}{x-9}\)
b, Ta có \(\dfrac{\dfrac{-3\sqrt{x}-3}{x-9}}{\dfrac{\sqrt{x}+1}{\sqrt{x}-3}}+\dfrac{1}{3}< 0\Leftrightarrow\dfrac{-3}{\sqrt{x}+3}+\dfrac{1}{3}< 0\)
\(\Rightarrow-9+\sqrt{x}+3< 0\Leftrightarrow\sqrt{x}-6< 0\Leftrightarrow x< 36\)
Kết hợp đk vậy 0 =< x < 36 ; x khác 9
Bài 11:
a \(B=\dfrac{2x+2\sqrt{x}-4+\sqrt{x}+7-x-4\sqrt{x}-3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{x-\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}=\dfrac{\sqrt{x}}{\sqrt{x}+3}\)
b: Để B là số nguyên thì \(\sqrt{x}+3-3⋮\sqrt{x}+3\)
\(\Leftrightarrow\sqrt{x}+3=3\)
=>x=0
