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

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

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

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

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

Hướng dẫn giải:

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

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

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

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

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

P=(1+x​1​)(x​+11​+x​−11​−x−12​)

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

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

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

P=(1+x​1​)(x​+11​+x​−11​−x−12​)

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

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

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

P=(1+x​1​)(x​+11​+x​−11​−x−12​)

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

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

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

P=(1+x​1​)(x​+11​+x​−11​−x−12​)

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

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

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

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=x2−x​1​:xx​+x+x​x​+1​

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

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

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

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​

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

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