5.
a, \(P=\left(\sqrt{x}-\dfrac{x+3}{\sqrt{x}+1}\right):\left(\dfrac{\sqrt{x}}{\sqrt{x}+1}-\dfrac{\sqrt{x}-9}{1-x}\right)\)
\(=\left(\dfrac{x+\sqrt{x}}{\sqrt{x}+1}-\dfrac{x+3}{\sqrt{x}+1}\right):\left[\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}+\dfrac{\sqrt{x}-9}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right]\)
\(=\dfrac{\sqrt{x}-3}{\sqrt{x}+1}:\dfrac{x-9}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{\sqrt{x}-3}{\sqrt{x}+1}.\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{\sqrt{x}-1}{\sqrt{x}+3}\)
6.
a, \(P=\left(\dfrac{x+1}{x+\sqrt{x}}-\dfrac{2}{\sqrt{x}+1}\right).\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(=\left[\dfrac{x+1}{\sqrt{x}\left(\sqrt{x}+1\right)}-\dfrac{2\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)}\right].\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(=\dfrac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}\left(\sqrt{x}+1\right)}.\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(=\dfrac{\sqrt{x}-1}{\sqrt{x}}\)
5.
b, \(P=\dfrac{\sqrt{x}-1}{\sqrt{x}+3}=\dfrac{1}{3}\)
\(\Leftrightarrow3\sqrt{x}-3=\sqrt{x}+3\)
\(\Leftrightarrow2\sqrt{x}=6\)
\(\Leftrightarrow x=9\left(l\right)\)
\(\Rightarrow\) Không tồn tại giá trị x thỏa mãn \(P=\dfrac{1}{3}\).
6.
b, \(2P=\dfrac{2\sqrt{x}-2}{\sqrt{x}}=1\)
\(\Leftrightarrow2\sqrt{x}-2=\sqrt{x}\)
\(\Leftrightarrow\sqrt{x}=2\)
\(\Leftrightarrow x=4\left(tm\right)\)
