Question

Сократите дробь: √(а^3-а)/(а-2а^(1/2)+1)


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Answer 1

$mathtt{sqrt{frac{a^3-a}{a-2a^{frac{1}{2}}+1}}=sqrt{frac{a(a^2-1)}{(a^{frac{1}{2}}-1)^2}}=sqrt{frac{a(a^2-1)(a^{frac{1}{2}}+1)^2}{(a^{frac{1}{2}}-1)^2(a^{frac{1}{2}}+1)^2}}=sqrt{frac{a(a+1)(a^{frac{1}{2}}+1)^2}{a-1}}=}\\mathtt{|a^{frac{1}{2}}+1|sqrt{frac{a^2+a}{a-1}},~aneq1}$