Question

упростите выражение, пожалуйста

Answer 1

$(\frac{\sqrt{a}+2 }{a+2\sqrt{a}+1 } -\frac{\sqrt{a}-2 }{a-1} )*\frac{\sqrt{a}+1 }{\sqrt{a} } =(\frac{\sqrt{a}+2 }{(\sqrt{a}+1)^{2} } +\frac{\sqrt{a}-2}{(\sqrt{a}-1)(\sqrt{a}+1)})*\frac{\sqrt{a}+1}{\sqrt{a}} =\\\\=\frac{(\sqrt{a}-1)(\sqrt{a}+2)-(\sqrt{a}+1)(\sqrt{a}-2)}{(\sqrt{a}-1)(\sqrt{a}+1)^{2} } *\frac{\sqrt{a}+1}{\sqrt{a}}=\frac{a+2\sqrt{a}-\sqrt{a}-2-(a-2\sqrt{a}+\sqrt{a}-2)}{(\sqrt{a}-1)(\sqrt{a}+1)} *\frac{1}{\sqrt{a}}=$

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