tex]...

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[tex] \frac{a \sqrt{a}+b \sqrt{b}}{(\sqrt{a} + \sqrt{b})(a-b)}+ \frac{2 \sqrt{b} }{ \sqrt{a} + \sqrt{b}}- \frac{\sqrt{ab} }{a-b} [/tex]

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inblu

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$\frac{a \sqrt{a}+b \sqrt{b}+2 \sqrt{b}(a-b)- \sqrt{ab}(\sqrt{a}+ \sqrt{b})}{( \sqrt{a}+ \sqrt{b})(a-b)}=\frac{a \sqrt{a}+b \sqrt{b}+2 a\sqrt{b}-2b \sqrt{b}- a\sqrt{b}-b\sqrt{a}}{( \sqrt{a}+ \sqrt{b})(a-b)}= \\=\frac{a \sqrt{a}-b \sqrt{b}+a\sqrt{b}-b \sqrt{a}}{( \sqrt{a}+ \sqrt{b})(a-b)}=\frac{ \sqrt{a}(a-b)+ \sqrt{b}(a-b)}{( \sqrt{a}+ \sqrt{b})(a-b)}= \frac{( \sqrt{a}+ \sqrt{b})(a-b)}{( \sqrt{a}+ \sqrt{b})(a-b)}=1$

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