241° Вправа 241Алгебра 8 клас Тарасенкова 2025 · § 7 · стор. 74

241. Розв’яжіть рівняння:

Дріб дорівнює нулю, якщо чисельник дорівнює нулю, а знаменник — ні: ${\displaystyle \frac{A}{B}=}$${\displaystyle 0}$, якщо ${\displaystyle A=}$${\displaystyle 0}$ і ${\displaystyle B\ne 0}$.

1) ${\displaystyle \frac{2x}{x+1}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle x+1\ne 0}$;

${\displaystyle x\ne -1}$;

${\displaystyle 2x=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 0}$;

2) ${\displaystyle \frac{x-3}{2x}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle 2x\ne 0}$;

${\displaystyle x\ne 0}$;

${\displaystyle x-3=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 3}$;

3) ${\displaystyle \frac{x-2}{x+2}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle x+2\ne 0}$;

${\displaystyle x\ne -2}$;

${\displaystyle x-2=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 2}$;

4) ${\displaystyle \frac{x+3}{x-3}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle x-3\ne 0}$;

${\displaystyle x\ne 3}$;

${\displaystyle x+3=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle -3}$;

5) ${\displaystyle \frac{x^2}{x^2+1}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle x}$ — будь-яке число, бо ${\displaystyle x^2+1>0}$;

${\displaystyle x^2=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 0}$;

6) ${\displaystyle \frac{x^2-1}{3x}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle 3x\ne 0}$;

${\displaystyle x\ne 0}$;

${\displaystyle (x-1)(x+1)=}$${\displaystyle 0}$;

${\displaystyle x-1=}$${\displaystyle 0}$ або ${\displaystyle x+1=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 1}$ або ${\displaystyle x=}$${\displaystyle -1}$;

7) ${\displaystyle \frac{3x^3}{x+3}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle x+3\ne 0}$;

${\displaystyle x\ne -3}$;

${\displaystyle 3x^3=}$${\displaystyle 0}$;

${\displaystyle x^3=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 0}$;

8) ${\displaystyle \frac{x-5}{5x}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle 5x\ne 0}$;

${\displaystyle x\ne 0}$;

${\displaystyle x-5=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 5}$.