Help me![tex] \frac{a}{ \sqrt{ab} +b} + \frac{b}{ \sqrt{ab}-a } - \frac{a+b}{ \sqrt{ab} } [/tex]. Created by pro100tabletk. algebra-ru

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

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

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