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[tex]\displaystyle\bf\\\Big(\frac{a}{\sqrt{a} +\sqrt{b} } -\frac{a\sqrt{a} }{a+b+2\sqrt{ab} } \Big):\Big(\frac{\sqrt{a} }{\sqrt{a}+\sqrt{b} } +\frac{a}{b-a} \Big)=\\\\\\\Big(\frac{a}{\sqrt{a} +\sqrt{b} }-\frac{a\sqrt{a} }{(\sqrt{a} +\sqrt{b} )^{2} } \Big):\Big(\frac{\sqrt{a} }{\sqrt{a} +\sqrt{b} } -\frac{a}{(\sqrt{a} +\sqrt{b} )(\sqrt{a} -\sqrt{b} )} \Big)=[/tex]

[tex]\displaystyle\bf\\=\frac{a\cdot(\sqrt{a}+\sqrt{b})-a\sqrt{a} }{(\sqrt{a} +\sqrt{b} )^{2} } :\frac{\sqrt{a} \cdot(\sqrt{a} -\sqrt{b} )-a}{(\sqrt{a} +\sqrt{b} )(\sqrt{a} -\sqrt{b}) } =\\\\\\=\frac{a\sqrt{a}+a\sqrt{b}-a\sqrt{a} }{(\sqrt{a} +\sqrt{b} )^{2} } :\frac{a -\sqrt{ab} -a}{(\sqrt{a} +\sqrt{b} )(\sqrt{a} -\sqrt{b}) } =\\\\\\=\frac{a\sqrt{b} }{(\sqrt{a} +\sqrt{b} )^{2} } :\frac{-\sqrt{ab} }{(\sqrt{a} +\sqrt{b} )(\sqrt{a} -\sqrt{b}) } =[/tex]

[tex]\displaystyle\bf\\=-\frac{a\sqrt{b} }{(\sqrt{a}+\sqrt{b})^{2} } \cdot\frac{(\sqrt{a} +\sqrt{b})(\sqrt{a} -\sqrt{b} )}{\sqrt{ab} } =-\frac{\sqrt{a} \cdot(\sqrt{a} -\sqrt{b} )}{\sqrt{a} +\sqrt{b} } =\\\\\\=\frac{\sqrt{ab} -a}{\sqrt{a} +\sqrt{b} }[/tex]

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