Помогите решить уравнение [tex] \frac{5x+9}{x}- \frac{7x-1}{x-1}=-2[/tex]. Created by CKyTepucT. matematika-ru

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Хуqожнuк ОДЗ:
x ≠ 0
x ≠ 1

Умножим всё уравнение на x(x - 1):
(5x + 9)(x - 1) - x(7x - 1) = -2x(x - 1)
(5x² - 5x + 9x - 9) - 7x² + x = -2x² + 2x
5x² - 7x² + 4x + x - 9 = -2x² + 2x
-2x² + 2x² + 5x - 2x = 9
3x = 9
x = 3
Ответ: x = 3.

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Dимасuk

Verified answer

$\frac{5x+9}{x} - \frac{7x-1}{x-1}=-2 \\ \\ \frac{(5x+9)(x-1) - x(7x-1))}{x(x-1)} = -\frac{2x(x-1)}{x(x-1)} \\ \\ \frac{5x^2+9x-5x-9-7x^2+x +2x^2-2x}{x(x-1)} =0 \\ \\ \frac{3x-9}{x(x-1)} =0 \\ \\ \begin{cases}
 3x-9=0 \\ x -1 \neq 0 \\ x \ne 0 \end{cases} \\ \begin{cases}
 3(x-3)=0 \\ x \neq 1 \\ x \ne 0 \end{cases} \\ \begin{cases}
 x=3 \\ x \neq 1 \\ x \ne 0 \end{cases} \\ \\ OTBET: 3$

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Answers & Comments

Verified answer

vstavte propushennye bukvy obyasnite ih napisanie 1 1 roskosh 2 hleb so

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kakoe iz proizvedenij a polozhitelno b otricatelno v ravno nulyu 1 1

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