B=(x​+3x​−x​−3x+1​+x−96x+x​​): (x​+3x​−3​−1)

\(= \left(\right. \frac{x}{\sqrt{x} + 3} - \frac{x + 1}{\sqrt{x} - 3} + \frac{6 x + \sqrt{x}}{x - 9} \left.\right) : \left(\right. \frac{\sqrt{x} - 3}{\sqrt{x} + 3} - 1 \left.\right)\)

\(= \frac{x \left(\right. \sqrt{x} - 3 \left.\right) - \left(\right. x + 1 \left.\right) \left(\right. \sqrt{x} + 3 \left.\right) + 6 x + \sqrt{x}}{x - 9} : \frac{\sqrt{x} - 3 - \sqrt{x} - 3}{\sqrt{x} + 3}\)

\(= \frac{- 3}{x - 9} : \frac{- 6}{\sqrt{x} + 3}\)

\(= \frac{- 3}{x - 9} . \frac{\sqrt{x} + 3}{- 6}\)

\(= \frac{1}{2 \left(\right. \sqrt{x} - 3 \left.\right)} .\)

P=x2−x​1​:xx​+x+x​x​+1​

\(= \frac{1}{\sqrt{x} \left(\right. x \sqrt{x} - 1 \left.\right)} : \frac{\sqrt{x} + 1}{\sqrt{x} \left(\right. x + \sqrt{x} + 1 \left.\right)}\)

\(= \frac{1}{\sqrt{x} \left(\right. x \sqrt{x} - 1 \left.\right)} . \frac{\sqrt{x} \left(\right. x + \sqrt{x} + 1 \left.\right)}{\sqrt{x} + 1}\)

\(= \frac{1}{x - 1}\).

V=(x​+21​+x​−21​).x​x​+2​

\(= \frac{\sqrt{x} - 2 + \sqrt{x} + 2}{x - 4} . \frac{\sqrt{x} + 2}{\sqrt{x}}\)

\(= \frac{2 \sqrt{x}}{x - 4} . \frac{\sqrt{x} + 2}{\sqrt{x}}\)

\(= \frac{2}{\sqrt{x} - 2}\).

P=(1+x​1​)(x​+11​+x​−11​−x−12​)

\(= \frac{\sqrt{x} + 1}{\sqrt{x}} . \frac{\sqrt{x} - 1 + \sqrt{x} + 1 - 2}{x - 1}\)

\(= \frac{\sqrt{x} + 1}{\sqrt{x}} . \frac{2 \left(\right. \sqrt{x} - 1 \left.\right)}{x - 1}\)

\(= \frac{2}{\sqrt{x}}\).

A=1−a22a2+4​−1−a​1​−1+a​1​

\(= \frac{2 a^{2} + 4}{1 - a^{2}} - \frac{1 + \sqrt{a} + 1 - \sqrt{a}}{1 - a}\)

\(= \frac{2 a^{2} + 4}{1 - a^{2}} - \frac{2}{1 - a}\)

\(= \frac{2 a^{2} + 4 - 2 \left(\right. 1 + a \left.\right)}{1 - a^{2}}\)

\(= \frac{2 a^{2} - 2 a + 2}{1 - a^{2}}\).

P=[x−x​−2x−x​+2​−x−2x​x​]:2−x​1−x​​

\(= \left[\right. \frac{x - \sqrt{x} + 2}{\left(\right. \sqrt{x} + 1 \left.\right) \left(\right. \sqrt{x} - 2 \left.\right)} - \frac{x}{\sqrt{x} \left(\right. \sqrt{x} - 2 \left.\right)} \left]\right. : \frac{1 - \sqrt{x}}{2 - \sqrt{x}}\)

\(= \frac{x \sqrt{x} - x + 2 \sqrt{x} - x \left(\right. \sqrt{x} + 1 \left.\right)}{\sqrt{x} \left(\right. \sqrt{x} + 1 \left.\right) \left(\right. \sqrt{x} - 2 \left.\right)} : \frac{1 - \sqrt{x}}{2 - \sqrt{x}}\)

\(= \frac{- 2 x + 2 \sqrt{x}}{\sqrt{x} \left(\right. \sqrt{x} + 1 \left.\right) \left(\right. \sqrt{x} - 2 \left.\right)} . \frac{2 - \sqrt{x}}{1 - \sqrt{x}}\)

\(= \frac{2 \sqrt{x} \left(\right. 1 - \sqrt{x} \left.\right)}{\sqrt{x} \left(\right. \sqrt{x} + 1 \left.\right) \left(\right. \sqrt{x} - 2 \left.\right)} . \frac{2 - \sqrt{x}}{1 - \sqrt{x}}\)

\(= \frac{- 2}{\sqrt{x} + 1} .\)

B=[x​−1x​​−x​(x​−1)1​].x​+11​

\(= \left[\right. \frac{x - 1}{\sqrt{x} \left(\right. \sqrt{x} - 1 \left.\right)} \left]\right. . \frac{1}{\sqrt{x} + 1}\)

\(= \frac{1}{\sqrt{x}}\).

a) \(2 \sqrt{\frac{2}{3}} - 4 \sqrt{\frac{3}{2}}\)

\(= 2 \sqrt{\frac{2.3}{3^{2}}} - 4 \sqrt{\frac{3.2}{2^{2}}}\)

\(= 2. \frac{\sqrt{6}}{3} - 2. \sqrt{6}\)

\(= - \frac{4 \sqrt{6}}{3}\).

b) \(\frac{5 \sqrt{48} - 3 \sqrt{27} + 2 \sqrt{12}}{\sqrt{3}}\)

\(= \frac{5 \sqrt{4^{2} . 3} - 3 \sqrt{3^{2} . 3} + 2 \sqrt{2^{2} . 3}}{\sqrt{3}}\)

\(= \frac{20 \sqrt{3} - 9 \sqrt{3} + 4 \sqrt{3}}{\sqrt{3}}\)

\(= \frac{15 \sqrt{3}}{\sqrt{3}} = 15\)

c) \(\frac{1}{3 + 2 \sqrt{2}} + \frac{4 \sqrt{2} - 4}{2 - \sqrt{2}}\)

\(= \frac{1. \left(\right. 3 - 2 \sqrt{2} \left.\right)}{\left(\right. 3 + 2 \sqrt{2} \left.\right) \left(\right. 3 - 2 \sqrt{2} \left.\right)} + \frac{4 \left(\right. \sqrt{2} - 1 \left.\right)}{\sqrt{2} \left(\right. \sqrt{2} - 1 \left.\right)}\)

\(= \frac{3 - 2 \sqrt{2}}{9 - 8} + \frac{4}{\sqrt{2}}\)

\(= 3 - 2 \sqrt{2} + 2 \sqrt{2}\)

\(= 3\).

a) \(\left(\right. \sqrt{\frac{4}{3}} + \sqrt{3} \left.\right) . \sqrt{6}\)

\(= \left(\right. \sqrt{\frac{4.3}{3^{2}}} + \sqrt{3} \left.\right) \sqrt{6}\)

\(= \left(\right. \frac{2 \sqrt{3}}{3} + \sqrt{3} \left.\right) \sqrt{6}\)

\(= \frac{2 \sqrt{3} . \sqrt{6}}{3} + \sqrt{3} . \sqrt{6}\)

\(= 2 \sqrt{2} + 3 \sqrt{2} = 5 \sqrt{2}\).

b) \(\left(\right. 1 - 2 \sqrt{5} \left.\right)^{2}\)

\(= 1 - 4 \sqrt{5} + \left(\right. 2 \sqrt{5} \left.\right)^{2}\)

\(= 1 - 4 \sqrt{5} + 20\)

\(= 21 - 4 \sqrt{5}\).

c) \(2 \sqrt{3} - \sqrt{27}\)

\(= 2 \sqrt{3} - 3 \sqrt{3}\)

\(= - \sqrt{3}\).

d) \(\sqrt{45} - \sqrt{20} + \sqrt{5}\)

\(= 3 \sqrt{5} - 2 \sqrt{5} + \sqrt{5}\)

\(= 2 \sqrt{5}\).

a) \(A = \frac{\sqrt{3}}{\sqrt{\sqrt{3} + 1} - 1} - \frac{\sqrt{3}}{\sqrt{\sqrt{3} + 1} + 1}\)

\(= \sqrt{3} \left[\right. \frac{\left(\right. \sqrt{\sqrt{3} + 1} + 1 \left.\right) - \left(\right. \sqrt{\sqrt{3} + 1} - 1 \left.\right)}{\left(\right. \sqrt{\sqrt{3} + 1} - 1 \left.\right) \left(\right. \sqrt{\sqrt{3} + 1} + 1 \left.\right)} \left]\right.\)

\(= \sqrt{3} . \frac{2}{\sqrt{3} + 1 - 1} = 2\).

b) \(\frac{15}{\sqrt{6} + 1} = \frac{15 \left(\right. \sqrt{6} - 1 \left.\right)}{6 - 1} = 3 \sqrt{6} - 3\);

\(\frac{4}{\sqrt{6} - 2} = 4 + 2 \sqrt{6}\);

\(\frac{12}{3 - \sqrt{6}} = 12 + 4 \sqrt{6}\).

Suy ra \(B = \left(\right. 3 \sqrt{6} - 3 + 4 + 2 \sqrt{6} - 12 - 4 \sqrt{6} \left.\right) \left(\right. \sqrt{6} + 11 \left.\right)\)

\(= \left(\right. \sqrt{6} + 11 \left.\right) \left(\right. \sqrt{6} - 11 \left.\right) = - 115\).

c) \(C = 4 \sqrt{20} - 3 \sqrt{125} + 5 \sqrt{45} - 15 \sqrt{\frac{1}{5}}\)

\(= 4.2 \sqrt{5} - 3.5 \sqrt{5} + 5.3 \sqrt{5} - 3 \sqrt{\frac{25}{5}}\)

\(= 8 \sqrt{5} - 15 \sqrt{5} - 3 \sqrt{5} + 15 \sqrt{5} = 5 \sqrt{5}\)