Решите уравнение........................................................ [tex] \frac{1}{4}*( \frac{1}{x+9}+ \frac{1}{x})= \frac{5}{6}- \frac{3}{x} [/tex]. Created by rrrrtttt01. algebra-ru

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July 2022 1 26 Report

Решите уравнение........................................................
[tex] \frac{1}{4}*( \frac{1}{x+9}+ \frac{1}{x})= \frac{5}{6}- \frac{3}{x} [/tex]

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Artem112

Verified answer

$\frac{1}{4}\cdot( \frac{1}{x+9}+ \frac{1}{x})= \frac{5}{6}- \frac{3}{x} , \ x \neq 0, \ x \neq 9
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 \frac{1}{4}\cdot \frac{x+x+9}{x(x+9)}= \frac{5}{6}- \frac{3}{x}
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 \frac{1}{4}\cdot \frac{2x+9}{x(x+9)}= \frac{5}{6}- \frac{3}{x} \ / \cdot12x(x+9)
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3(2x+9)=2x(x+9)\cdot5-12(x+9)\cdot3
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6x+27=10x(x+9)-36(x+9)
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6x+27=10x^2+90x-36x-324
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10x^2+48x-351=0
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D_1=24^2-10\cdot(-351)=576+3510=4086
\\\
x= \frac{-24\pm \sqrt{4086} }{10}$

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