Bài 1:
c: \(\left(\frac{\sqrt{a}+1}{\sqrt{a}-1}-\frac{\sqrt{a}-1}{\sqrt{a}+1}+4\sqrt{a}\right)\left(\sqrt{a}-\frac{1}{\sqrt{a}}\right)\)
\(=\left(\frac{\left(\sqrt{a}+1\right)^2-\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}+4\sqrt{a}\right)\cdot\frac{a-1}{\sqrt{a}}\)
\(=\left(\frac{a+2\sqrt{a}+1-a+2\sqrt{a}-1}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}+4\sqrt{a}\right)\cdot\frac{a-1}{\sqrt{a}}\)
\(=4\sqrt{a}\left(\frac{1}{a-1}+1\right)\cdot\frac{a-1}{\sqrt{a}}=4\cdot\left(a-1\right)\cdot\frac{1+a-1}{a-1}=4a\)
d: \(\left(\frac{1}{\sqrt{a}-1}-\frac{1}{\sqrt{a}}\right):\left(\frac{\sqrt{a}+1}{\sqrt{a}-2}-\frac{\sqrt{a}-1}{\sqrt{a}+2}\right)\)
\(=\frac{\sqrt{a}-\left(\sqrt{a}-1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)}:\frac{\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\right)-\left(\sqrt{a}-1\right)\left(\sqrt{a}-2\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\)
\(=\frac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\frac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}{a+3\sqrt{a}+2-a+3\sqrt{a}+2}=\frac{a-4}{6\sqrt{a}\cdot\sqrt{a}\left(\sqrt{a}-1\right)}\)
f: \(\frac{a-3\sqrt{a}}{\sqrt{a}-3}-\frac{a+4\sqrt{a}+3}{\sqrt{a}+3}\)
\(=\frac{\sqrt{a}\left(\sqrt{a}-3\right)}{\sqrt{a}-3}-\frac{\left(\sqrt{a}+3\right)\left(\sqrt{a}+1\right)}{\sqrt{a}+3}\)
\(=\sqrt{a}-\left(\sqrt{a}+1\right)=-1\)
g: \(\left(\frac{\sqrt{a}}{3+\sqrt{a}}+\frac{a+9}{9-a}\right):\left(\frac{3\sqrt{a}+1}{a-3\sqrt{a}}-\frac{1}{\sqrt{a}}\right)\)
\(=\frac{\sqrt{a}\left(\sqrt{a}-3\right)-a-9}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-3\right)}:\frac{3\sqrt{a}+1-\sqrt{a}+3}{\sqrt{a}\left(\sqrt{a}-3\right)}\)
\(=\frac{-3\sqrt{a}-9}{\left(\sqrt{a}-3\right)\left(\sqrt{a}+3\right)}\cdot\frac{\sqrt{a}\left(\sqrt{a}-3\right)}{2\sqrt{a}+4}=\frac{-3\left(\sqrt{a}+1\right)}{\sqrt{a}+3}\cdot\frac{\sqrt{a}}{2\sqrt{a}+4}=-\frac{3\sqrt{a}}{2\sqrt{a}+4}\)
Bài 2:
a: \(A=\frac{2\sqrt{x}-9}{x-5\sqrt{x}+6}-\frac{\sqrt{x}+3}{\sqrt{x}-2}-\frac{2\sqrt{x}+1}{3-\sqrt{x}}\)
\(=\frac{2\sqrt{x}-9-\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)+\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
\(=\frac{2\sqrt{x}-9-x+9+\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}=\frac{-\sqrt{x}\left(\sqrt{x}-2\right)+\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
\(=\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}=\frac{\sqrt{x}+1}{\sqrt{x}-3}\)
