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[svetoslav80]

[tex]\frac{a^{\frac{1}{ 2}} }{ \sqrt{a}-1 } = \frac{\sqrt{a} }{ \sqrt{a}-1 }.\frac{\sqrt{a}+1}{\sqrt{a}+1 } = \frac{\sqrt{a}(\sqrt{a}+1) }{a-1 } = \frac{a+\sqrt{a} }{a-1 }[/tex]
[tex]=> \frac{a}{1-a } + \frac{a^{\frac{1}{ 2}} }{ \sqrt{a}-1 } = \frac{a}{1-a } + \frac{a+\sqrt{a} }{a-1 } = \frac{a+\sqrt{a} }{a-1 } - \frac{a}{a-1 } = \frac{a+\sqrt{a} -a}{a-1 } = \frac{\sqrt{a} }{a-1 }[/tex]