5.
ĐKXĐ: \(x\ge0;x\ne4;x\ne9\)
\(T=\dfrac{x-6\sqrt{x}+9}{\sqrt{x}-3}-\dfrac{x-4}{\sqrt{x}-2}=\dfrac{\left(\sqrt{x}-3\right)^2}{\sqrt{x}-3}-\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\sqrt{x}-2}\)
\(=\sqrt{x}-3-\left(\sqrt{x}+2\right)\)
\(=-5\)
6.
ĐKXĐ: \(x>0;x\ne1\)
\(A=\left(\dfrac{x-1}{2\sqrt{x}}\right)\left(\dfrac{\left(x-\sqrt{x}\right)\left(\sqrt{x}-1\right)-\left(x+\sqrt{x}\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right)\)
\(=\left(\dfrac{x-1}{2\sqrt{x}}\right)\left(\dfrac{-2x\left(\sqrt{x}+1\right)}{x-1}\right)\)
\(=-\sqrt{x}\left(\sqrt{x}+1\right)=-x-\sqrt{x}\)
b.
\(A>-6\Leftrightarrow-x-\sqrt{x}>-6\)
\(\Leftrightarrow x+\sqrt{x}-6< 0\)
\(\Leftrightarrow\left(\sqrt{x}-2\right)\left(\sqrt{x}+3\right)< 0\)
\(\Leftrightarrow\sqrt{x}-2< 0\)
\(\Leftrightarrow x< 4\)
Kết hợp ĐKXĐ \(\Rightarrow\left\{{}\begin{matrix}0< x< 4\\x\ne1\end{matrix}\right.\)
7.
\(A=\dfrac{x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}+\dfrac{\sqrt{x}-2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(=\dfrac{x+\sqrt{x}+2+\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{x+2\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(=\dfrac{\sqrt{x}}{\sqrt{x}-2}\)
b.
\(A=\dfrac{\sqrt{25}}{\sqrt{25}-2}=\dfrac{5}{3}\)
c.
\(A=-\dfrac{1}{3}\Leftrightarrow\dfrac{\sqrt{x}}{\sqrt{x}-2}=-\dfrac{1}{3}\)
\(\Rightarrow3\sqrt{x}=-\sqrt{x}+2\)
\(\Leftrightarrow\sqrt{x}=\dfrac{1}{2}\Rightarrow x=\dfrac{1}{4}\)
