\(\sqrt{\dfrac{3x^2-3x-2x+2}{4x^2-12x+9}}=\sqrt{\dfrac{\left(3x-2\right)\left(x-1\right)}{\left(2x-3\right)^2}}\)

đk \(\left\{{}\begin{matrix}\left(3x-2\right)\left(x-1\right)>0\\2x-3\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>1\\x< \dfrac{2}{3}\\x\ne\dfrac{3}{2}\end{matrix}\right.\)

\(=\sqrt{2}-1-\sqrt{2}-1-2=-4\)

\(ĐKXĐ:x\ge0\)

\(4x-2\sqrt{x}=0\)

\(\Leftrightarrow2\sqrt{x}\left(2\sqrt{x}-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=0\\2\sqrt{x}-1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(tm\right)\\x=\dfrac{1}{4}\left(tm\right)\end{matrix}\right.\)

đk x >= 0 

\(2\sqrt{x}\left(2\sqrt{x}-1\right)=0\Leftrightarrow x=0;x=\dfrac{1}{4}\left(tm\right)\)

a, đk \(\left\{{}\begin{matrix}x^2-4x+4\ge0\\x-3\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(x-2\right)^2\ge0\left(dung\right)\\x\ne3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\in R\\x\ne3\end{matrix}\right.\)

b, đk \(\left\{{}\begin{matrix}2x-3>0\\x-7>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>\dfrac{3}{2}\\x>7\end{matrix}\right.\Leftrightarrow x>7\)

c, đk \(x-10\sqrt{x}+25>0\Leftrightarrow\left(\sqrt{x}-5\right)^2>0\Rightarrow x\ne25\)

\(7-4\sqrt{3}=7-2.2\sqrt{3}=4-2.2\sqrt{3}+3=\left(2-\sqrt{3}\right)^2=\left(\sqrt{3}-2\right)^2\)

a, \(=\sqrt{\left(2-\sqrt{3}\right)^2}-\sqrt{\left(2+\sqrt{3}\right)^2}=2-\sqrt{3}-2-\sqrt{3}=-2\sqrt{3}\)

b, \(=\sqrt{\left(\sqrt{5}-1\right)^2}+\sqrt{\left(\sqrt{5}+1\right)^2}=\sqrt{5}-1+\sqrt{5}+1=2\sqrt{5}\)

c, \(=\sqrt{\left(2\sqrt{2}+1\right)^2}-\sqrt{\left(\sqrt{2}-1\right)^2}=2\sqrt{2}+1-\sqrt{2}+1=\sqrt{2}+2\)