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June 2022 1 26 Report

Сократите дробь :
а) x-18/[tex] \sqrt{x} [/tex] + [tex]3\sqrt{2} [/tex]

б) 4[tex] a^{2} [/tex] - [tex] 4a \sqrt{3b} [/tex] + 3b / [tex] 2a\sqrt{b} [/tex] - [tex] b\sqrt{3} [/tex]

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NNNLLL54

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$1)\; \; \; \frac{x-18}{\sqrt{x}+3\sqrt2} = \frac{(\sqrt{x})^2-(\sqrt{18})^2}{\sqrt{x}+\sqrt{9\cdot 2}} = \frac{(\sqrt{x}-\sqrt{18})(\sqrt{x}+\sqrt{18})}{\sqrt{x}+\sqrt{18}} =\\\\=\sqrt{x}-\sqrt{18}=\sqrt{x}-3\sqrt2\\\\2)\; \; \; \frac{4a^2-4a\sqrt{3b}+3b}{2a\sqrt{b}-b\sqrt3} = \frac{(2a)^2-2\cdot (2a)\cdot \sqrt{3b}+(\sqrt{3b})^2}{\sqrt{b}\cdot (2a-\sqrt{b}\cdot \sqrt3)} =\\\\=\frac{(2a-\sqrt{3b})^2}{\sqrt{b}\cdot (2a-\sqrt{3b})} =\frac{2a-\sqrt{3b}}{\sqrt{b}}$

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