205 Вправа 205Алгебра 8 клас Бевз 2025 · § 4 · стор. 42

Умова

Розв’яжи рівняння.

205. Розв’яжи рівняння.

а) $\frac{12 x}{4 x^{2} - 9} + \frac{2 x - 3}{4 x + 6} + \frac{2 x + 3}{6 x - 9} =$ $0$ ;

$\frac{{12 x}^{∖ 6}}{(2 x - 3) (2 x + 3)} + \frac{{2 x - 3}^{∖ 3 (2 x - 3)}}{2 (2 x + 3)} + \frac{{2 x + 3}^{∖ 2 (2 x + 3)}}{3 (2 x - 3)}$ =

= $\frac{72 x + 3 (2 x - 3) (2 x - 3) + 2 (2 x + 3) (2 x + 3)}{6 (2 x - 3) (2 x + 3)}$ =

= $\frac{72 x + 12 x^{2} - 36 x + 27 + 8 x^{2} + 24 x + 18}{6 (2 x - 3) (2 x + 3)}$ =

= $\frac{20 x^{2} + 60 x + 45}{6 (2 x - 3) (2 x + 3)}$ =0;

${\begin{aligned} 5 {(2 x + 3)}^{2} = 0 \\ 6 (2 x - 3) (2 x + 3) \neq 0 \end{aligned}$ ;

${\begin{aligned} x = - \frac{3}{2} \\ x \neq - \frac{3}{2}, x \neq \frac{3}{2} \end{aligned}$ ;

коренів немає;

б) $\frac{1}{x - 2} - \frac{x - 2}{x^{2} + 2 x + 4} - \frac{5 x}{x^{3} - 8} =$ $0$ ;

$\frac{1^{∖ x^{2} + 2 x + 4}}{x - 2} - \frac{{x - 2}^{∖ x - 2}}{x^{2} + 2 x + 4} - \frac{5 x}{(x - 2) (x^{2} + 2 x + 4)}$ =

= $\frac{x^{2} + 2 x + 4 - (x - 2) (x - 2) - 5 x}{(x - 2) (x^{2} + 2 x + 4)}$ =

= $\frac{x^{2} + 2 x + 4 - x^{2} + 4 x - 4 - 5 x}{(x - 2) (x^{2} + 2 x + 4)} =$ $\frac{x}{(x - 2) (x^{2} + 2 x + 4)}$ =0;

${\begin{aligned} x = 0 \\ (x - 2) (x^{2} + 2 x + 4) \neq 0 \end{aligned}$ ;

${\begin{aligned} x = 0 \\ x \neq 2 \end{aligned}$ ;

$x =$ $0$ .