\(P=\dfrac{1}{\sqrt{x}-2}+\dfrac{2}{\sqrt{x}+2}-\dfrac{\sqrt{x}-6}{x-4}\)
a) \(ĐKXĐ:x\ge0,x\ne4\)
\(P=\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{2\sqrt{x}-4}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}-\dfrac{\sqrt{x}-6}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(P=\dfrac{\sqrt{x}+2+2\sqrt{x}-4-\sqrt{x}+6}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(P=\dfrac{2\sqrt{x}+4}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(P=\dfrac{2\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(P=\dfrac{2}{\sqrt{x}-2}\)
b) Thay \(x=\dfrac{1}{4}\) vào P
\(\Leftrightarrow P=\dfrac{2}{\sqrt{\dfrac{1}{4}}-2}\)
\(P=\dfrac{2}{\dfrac{1}{2}-2}\)
\(P=2.-\dfrac{2}{3}=-\dfrac{4}{3}\)
c) \(P< 0\Leftrightarrow\dfrac{2}{\sqrt{x}-2}< 0\)
\(\Leftrightarrow\sqrt{x}-2< 0\) ( vì 2 > 0 )
\(\Leftrightarrow\sqrt{x}< 2\)
\(\Leftrightarrow x< 4\)
_Chúc bạn học tốt_
