Mathematics: Rationalize the denominator and simplify: (sqrt= square root) 2 sqrt X - 3 sqrt Y sqrt X + sqrt Y

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Rationalize the denominator and simplify: (sqrt=

Ответ:

u8p4

05.02.2022

Mathematics

Step-by-step explanation:

$Domain:\ x0\ \wedge\ y0$

$\dfrac{2\sqrt{x}-3\sqrt{y}}{\sqrt{x}+\sqrt{y}}\qquad|\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=\dfrac{2\sqrt{x}-3\sqrt{y}}{\sqrt{x}+\sqrt{y}}\cdot\dfrac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}=\dfrac{(2\sqrt{x}-3\sqrt{y})(\sqrt{x}-\sqrt{y})}{(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})}\\\\\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=\dfrac{(2\sqrt{x})(\sqrt{x})+(2\sqrt{x})(-\sqrt{y})+(-3\sqrt{y})(\sqrt{x})+(-3\sqrt{y})(-\sqrt{y})}{(\sqrt{x})^2-(\sqrt{y})^2}$

$\text{use}\ (\sqrt{a})^2=a\ \text{and}\ (\sqrt{a})(\sqrt{a})=a\ \text{for}\ a\geq0\\\text{and}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\=\dfrac{2x-2\sqrt{xy}-3\sqrt{xy}+3y}{x-y}\qquad|\text{combine like terms}\\\\=\dfrac{2x+3y-5\sqrt{xy}}{x-y}$

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Ответ:

jadajohnson14

10.03.2023

Mathematics

DAYO I gots no points help me homie ФФ

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Rationalize the denominator and simplify: (sqrt= square root) 2 sqrt X - 3 sqrt Y

sqrt X + sqrt Y

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