Решите уравнение:[tex] \\ \frac{5x+6}{ x^{2} -4}+ \frac{3x+5}{x+2}= \frac{x}{x-2} \\ A)1 \\ B)2 \\ C)3 \\ D)-2 \\ E)-1[/tex]. Created by madinashaizaman. algebra-ru

ОДЗ: или ∉ ОДЗОтвет:A)

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Решите уравнение:[tex] \\ \frac{5x+6}{ x^{2} -4}+ \frac{3x+5}{x+2}= \frac{x}{x-2} \\ A)1 \\ B)2 \\ C)3 \\ D)-2 \\ E)-1[/tex]

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mukus13

Verified answer

$\frac{5x+6}{ x^{2} -4} + \frac{3x+5}{x+2} = \frac{x}{x-2}$

$\frac{5x+6}{ (x-2)(x+2)} + \frac{3x+5}{x+2} - \frac{x}{x-2} =0$

$\frac{5x+6+(3x+5)(x-2)-x(x+2)}{(x+2)(x-2)} =0$

ОДЗ: $(x+2)(x-2) \neq 0$
$x \neq -2$ или $x \neq 2$

$5x+6+(3x+5)(x-2)-x(x+2) =0$

$5x+6+3 x^{2} -6x+5x-10- x^{2} -2x=0$

$2 x^{2} +2x-4=0$

$x^{2} +x-2=0$

$D=1+8=9$
$x_1=1$
$x_2=-2$ ∉ ОДЗ

Ответ:A) $1$

7 votes Thanks 3

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