4) \(\dfrac{x-\sqrt{x}-2\sqrt{x}+2}{x-1}\)
\(=\dfrac{\left(x-\sqrt{x}\right)-\left(2\sqrt{x}-2\right)}{x-1}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)-2\left(\sqrt{x}-1\right)}{x-1}\)
\(=\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}{x-1}\)
\(=\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\)
5) \(\dfrac{x+4}{x\sqrt{x}+2x-\sqrt{x}-2}\)
\(=\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}{\left(x\sqrt{x}+2x\right)-\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}{x\left(\sqrt{x}+2\right)-\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{\sqrt{x}-2}{\sqrt{x}-1}\)
6) \(\dfrac{\sqrt{xy}-3\sqrt{y}}{x\sqrt{y}-5\sqrt{xy}+6\sqrt{y}}\)
\(=\dfrac{\sqrt{y}\left(\sqrt{x}-3\right)}{\sqrt{y}\left(x-5\sqrt{x}+6\right)}\)
\(=\dfrac{\sqrt{x}-3}{x-2\sqrt{x}-3\sqrt{x}+6}\)
\(=\dfrac{\sqrt{x}-3}{\sqrt{x}\left(\sqrt{x}-2\right)-3\left(\sqrt{x}-2\right)}\)
\(=\dfrac{\sqrt{x}-3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{1}{\sqrt{x}-2}\)
7) \(\left(2+\dfrac{a-2\sqrt{a}}{\sqrt{a}-2}\right)\left(2+\dfrac{a-\sqrt{a}}{\sqrt{a}-1}\right)\)
\(=\left(2+\dfrac{\sqrt{a}\left(\sqrt{a}-2\right)}{\sqrt{a}-2}\right)\left(2+\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)\)
\(=\left(2+\sqrt{a}\right)\left(2+\sqrt{a}\right)\)
\(=\left(2+\sqrt{a}\right)^2\)
\(=4+4\sqrt{a}+a\)
4: \(=\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}{x-1}\)
\(=\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\)
5: \(=\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(x-1\right)}=\dfrac{\sqrt{x}-2}{x-1}\)
6: \(=\dfrac{\sqrt{y}\left(\sqrt{x}-3\right)}{\sqrt{y}\left(x-5\sqrt{x}+6\right)}=\dfrac{\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\)
\(=\dfrac{1}{\sqrt{x}-2}\)
7: \(=\left(2+\dfrac{\sqrt{a}\left(\sqrt{a}-2\right)}{\sqrt{a}-2}\right)\cdot\left(2+\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)\)
=(2+căn a)(2+căn a)
=4+4căn a+a
2) 4) \(\dfrac{x-\sqrt{x}-2\sqrt{x}+2}{x-1}=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)-2\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\)
5) \(\dfrac{x-4}{x\sqrt{x}+2x-\sqrt{x}-2}=\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{x\left(\sqrt{x}+2\right)-\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+2\right)\left(x-1\right)}=\dfrac{\sqrt{x}-2}{x-1}\)
6) \(\dfrac{\sqrt{xy}-3\sqrt{y}}{\sqrt{y}\left(x-5\sqrt{x}+6\right)}=\dfrac{\sqrt{y}\left(\sqrt[]{x}-3\right)}{\sqrt{y}\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}=\dfrac{1}{\sqrt{x}-2}\)
7) \(\left(2+\dfrac{a-2\sqrt{a}}{\sqrt{a}-2}\right)\left(2+\dfrac{a-\sqrt{a}}{\sqrt{a}-1}\right)\)
\(=\left(2+\dfrac{\sqrt{a}\left(\sqrt{a}-2\right)}{\sqrt{a}-2}\right)\left(2+\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)\)
\(=\left(2+\sqrt{a}\right)\left(2+\sqrt{a}\right)=\left(2+\sqrt{a}\right)^2\)
