19 срочно пожалуйста как решить.. Created by bondarenkonekitaaaa. algebra-ru

19 срочно пожалуйста как решить...

elena20092

$\frac{a-1}{a+a^{1/2}+1}:\frac{a^{1/2}+1}{a^{3/2}-1}=\frac{(a^{1/2}-1)(a^{1/2}+1)}{a+a^{1/2}+1}\cdot \frac{(a^{1/2}-1)(a+a^{1/2}+1)}{a^{1/2}+1}=(a^{1/2}-1)^2$

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Verified answer

(а - 1)/(а + а^0.5 + 1) : (a^0.5 + 1)/(a^1.5 - 1) =

= (a^0.5 -1)(a^0.5 + 1)/(а + а^0.5 + 1) · ((a^0.5 - 1)·(а + а^0.5 + 1))/(a^0.5 + 1) =

= (a^0.5 - 1) · (a^0.5 - 1) = (a^0.5 - 1)² или можно ещё записать так:

а - 2a^0.5 + 1

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