Question

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Answer 1

$Big(dfrac{8}{sqrt{x}-1}+dfrac{sqrt[4]{x}+1}{sqrt[4]{x}-1}-dfrac{sqrt[4]{x}+3}{sqrt[4]{x}+1}Big):dfrac{3}{sqrt{x}-1}=\ \ \ =Big(dfrac{8}{sqrt{x}-1}+dfrac{(sqrt[4]{x}+1)^2-(sqrt[4]{x}+3)(sqrt[4]{x}-1)}{(sqrt[4]{x}-1)cdot (sqrt[4]{x}+1)}Big)cdot dfrac{sqrt{x}-1}{3}=\ \ \=Big(dfrac{8}{sqrt{x}-1}+dfrac{sqrt{x}+2sqrt[4]{x}+1-(sqrt{x}-sqrt[4]{x}+3sqrt[4]{x}-3)}{sqrt{x}-1}Big)cdot dfrac{sqrt{x}-1}{3}=$

$=Big(dfrac{8}{sqrt{x}-1}+dfrac{sqrt{x}+2sqrt[4]{x}+1-sqrt{x}+sqrt[4]{x}-3sqrt[4]{x}+3}{sqrt{x}-1}Big)cdot dfrac{sqrt{x}-1}{3}=\ \ \ =Big(dfrac{8}{sqrt{x}-1}+dfrac{4}{sqrt{x}-1}Big)cdot dfrac{sqrt{x}-1}{3}=\ \ \ =dfrac{12}{sqrt{x}-1}cdot dfrac{sqrt{x}-1}{3}=4$

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Использованы формулы

$sqrt[4]{x}^2=sqrt{x}\ \(a+b)^2=a^2+2ab+b^2 \ \(a-b)(a+b)=a^2-b^2$