(1/$\sqrt{a}$+1-1/a$\sqrt{a})*$\sqrt{a}-1/a+2$\sqrt{a}+1

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1. \(\begin{array}{l} (\frac{1}{{\sqrt a + 1}} – \frac{1}{{a\sqrt a }})(\frac{{\sqrt a – 1}}{{a + 2\sqrt a + 1}})\\ = \frac{{a\sqrt a – \sqrt a – 1}}{{a\sqrt a (\sqrt a + 1)}}.\frac{{\sqrt a – 1}}{{{{(\sqrt a + 1)}^2}}}\\ = \frac{{{a^2} – a\sqrt a – a + \sqrt a – \sqrt a + 1}}{{a\sqrt a {{(\sqrt a + 1)}^3}}}\\ = \frac{{{a^2} – a\sqrt a – a + 1}}{{a\sqrt a {{(\sqrt a + 1)}^3}}}\\ = \frac{{a\sqrt a (\sqrt a – 1) – (\sqrt a – 1)(\sqrt a + 1)}}{{a\sqrt a {{(\sqrt a + 1)}^3}}}\\ = \frac{{(a\sqrt a – \sqrt a – 1)(\sqrt a – 1)}}{{a\sqrt a {{(\sqrt a + 1)}^3}}} \end{array}\)

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2. \(\begin{array}{l}
   (\frac{1}{{\sqrt a + 1}} – \frac{1}{{a\sqrt a }})(\frac{{\sqrt a – 1}}{{a + 2\sqrt a + 1}})\\
   = \frac{{a\sqrt a – \sqrt a – 1}}{{a\sqrt a (\sqrt a + 1)}}.\frac{{\sqrt a – 1}}{{{{(\sqrt a + 1)}^2}}}\\
   = \frac{{{a^2} – a\sqrt a – a + \sqrt a – \sqrt a + 1}}{{a\sqrt a {{(\sqrt a + 1)}^3}}}\\
   = \frac{{{a^2} – a\sqrt a – a + 1}}{{a\sqrt a {{(\sqrt a + 1)}^3}}}\\
   = \frac{{a\sqrt a (\sqrt a – 1) – (\sqrt a – 1)(\sqrt a + 1)}}{{a\sqrt a {{(\sqrt a + 1)}^3}}}\\
   = \frac{{(a\sqrt a – \sqrt a – 1)(\sqrt a – 1)}}{{a\sqrt a {{(\sqrt a + 1)}^3}}}
   \end{array}\)

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