V=(x​+21​+x​−21​).x​x​+2​

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

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

\(= \frac{2}{\sqrt{�} - 2}\).

P=x2−x​1​:xx​+x+x​x​+1​

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

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

\(= \frac{1}{� - 1}\).

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

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

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

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

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

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

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

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

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

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

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

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

P=(x​+1x​​+x​−1x​​)(x​−x​1​)

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

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

P=(x​+1x​​+x​−1x​​)(x​−x​1​)

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

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

P=(x​+1x​​+x​−1x​​)(x​−x​1​)

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

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

P=x+2x​x+2​−x​1​+x​+21​

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

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

A=1−a22a2+4​−1−a​1​−1+a​1​

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

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

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

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

A=1−a22a2+4​−1−a​1​−1+a​1​

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

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

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

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