Question

ПОМОГИТЕ Упростите выражение:

Answer 1

Ответ:

$(\frac{8}{\sqrt{x}-1}+\frac{\sqrt[4]{x}+1}{\sqrt[4]{x}-1}-\frac{\sqrt[4]{x}+3}{\sqrt[4]{x}+1}):\frac{3}{\sqrt{x}-1} = \\= (\frac{8(\sqrt{x}-1) + (\sqrt{x}-1)(\sqrt[4]{x}+1)^2-(\sqrt{x}-1)(\sqrt[4]{x}-1)(\sqrt[4]{x}+3)}{(\sqrt{x}-1)^2}):\frac{3}{\sqrt{x}-1} = \\\\= \frac{(\sqrt{x}-1)(8+(\sqrt[4]{x}+1)^2-(\sqrt[4]{x}-1)(\sqrt[4]{x}+3))}{3(\sqrt{x}-1)} =\\\\= \frac{8+\sqrt{x}+2\sqrt[4]{x}+1-\sqrt{x}-2\sqrt[4]{x}+3}{3} = \\\\= \frac{12}{3} = 4;$