Question

нужно сократить:
a-5
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a+2√5a+5

Answer 1

$\frac{a-5}{a+2\sqrt{5a}+5}= \\\\ =\frac{(\sqrt{a})-\sqrt{5})\cdot (\sqrt{a}+\sqrt{5})}{{(\sqrt{a}+\sqrt{5})}^{2}}= \\\\ =\frac{\sqrt{a}-\sqrt{5}}{\sqrt{a}+\sqrt{5}}= \\\\ = \frac{\sqrt{a}-\sqrt{5}}{\sqrt{a}+\sqrt{5}}\cdot \frac{\sqrt{a}-\sqrt{5}}{\sqrt{a}-\sqrt{5}}= \\\\ =\frac{(\sqrt{a}-\sqrt{5})\cdot (\sqrt{a}-\sqrt{5})}{(\sqrt{a}+\sqrt{5})\cdot (\sqrt{a}-\sqrt{5})}= \\\\ =\frac{{(\sqrt{a}-\sqrt{5})}^{2}}{a-5}= \\\\ =\frac{a-2\sqrt{5a}+5}{a-5}$