244° Вправа 244Алгебра 8 клас Тарасенкова 2025 · § 7 · стор. 74

244. Розв’яжіть рівняння:

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

ОДЗ: ${\displaystyle x^2-1\ne 0}$;

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

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

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

${\displaystyle x=}$${\displaystyle 1}$ — не задовольняє ОДЗ;

коренів немає;

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

ОДЗ: ${\displaystyle x^2-4\ne 0}$;

${\displaystyle (x-2)(x+2)\ne 0}$;

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

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

${\displaystyle x=}$${\displaystyle -2}$ — не задовольняє ОДЗ;

коренів немає;

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

ОДЗ: ${\displaystyle (x-1)(x+1)\ne 0}$;

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

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

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

${\displaystyle x=}$${\displaystyle -1}$ — не задовольняє ОДЗ;

коренів немає;

4) ${\displaystyle \frac{3x-6}{x^2-4}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle (x-2)(x+2)\ne 0}$;

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

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

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

${\displaystyle x=}$${\displaystyle 2}$ — не задовольняє ОДЗ;

коренів немає;

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

ОДЗ: ${\displaystyle x-1\ne 0}$;

${\displaystyle x\ne 1}$;

${\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}$;

${\displaystyle x=}$${\displaystyle 1}$ — не задовольняє ОДЗ;

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

6) ${\displaystyle \frac{x^2-4}{x-2}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle x-2\ne 0}$;

${\displaystyle x\ne 2}$;

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

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

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

${\displaystyle x=}$${\displaystyle 2}$ — не задовольняє ОДЗ;

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

7) ${\displaystyle \frac{x^2-16}{x-4}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle x-4\ne 0}$;

${\displaystyle x\ne 4}$;

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

${\displaystyle x-4=}$${\displaystyle 0}$ або ${\displaystyle x+4=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 4}$ або ${\displaystyle x=}$${\displaystyle -4}$;

${\displaystyle x=}$${\displaystyle 4}$ — не задовольняє ОДЗ;

${\displaystyle x=}$${\displaystyle -4}$;

8) ${\displaystyle \frac{x^2-16}{3x+12}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle 3x+12\ne 0}$;

${\displaystyle 3(x+4)\ne 0}$;

${\displaystyle x\ne -4}$;

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

${\displaystyle x-4=}$${\displaystyle 0}$ або ${\displaystyle x+4=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 4}$ або ${\displaystyle x=}$${\displaystyle -4}$;

${\displaystyle x=}$${\displaystyle -4}$ — не задовольняє ОДЗ;

${\displaystyle x=}$${\displaystyle 4}$.