Question

нужно сократить:
a-5
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a+2√5a+5

Answer 1

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