\(x=9\Rightarrow A=\dfrac{\sqrt{9}+1}{\sqrt{9}-1}=\dfrac{3+1}{3-1}=2\)
b.
\(B=\left(\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right).\left(\dfrac{\sqrt{x}-1}{\sqrt{x}}\right)\)
\(=\left(\dfrac{x+2\sqrt{x}+1-x+2\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right).\left(\dfrac{\sqrt{x}-1}{\sqrt{x}}\right)\)
\(=\dfrac{4\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{4}{\sqrt{x}+1}\)
c. Do \(\sqrt{x}+1>0;\forall x\Rightarrow\dfrac{4}{\sqrt{x}+1}>0;\forall x\Rightarrow B>0\)
Để A và B trái dấu \(\Rightarrow A< 0\)
\(\Rightarrow\dfrac{\sqrt{x}+1}{\sqrt{x}-1}< 0\Rightarrow\sqrt{x}-1< 0\)
\(\Rightarrow x< 1\)
Kết hợp ĐKXĐ \(\Rightarrow0< x< 1\)
