218° Вправа 218Алгебра 8 клас Тарасенкова 2025 · § 6 · стор. 65

218. Виконайте ділення.

1) ${\displaystyle (x-3):\frac{x-3}{9}=}$${\displaystyle (x-3)\cdot \frac{9}{x-3}=}$${\displaystyle \frac{\cancel{\left(x-3\right)}\cdot 9}{\cancel{x-3}}=}$${\displaystyle 9}$;

2) ${\displaystyle (3x-1):\frac{3x-1}{3}=}$${\displaystyle (3x-1)\cdot \frac{3}{3x-1}=}$${\displaystyle 3}$;

3) ${\displaystyle (2x-2):\frac{x-1}{8}=}$${\displaystyle 2(x-1)\cdot \frac{8}{x-1}=}$${\displaystyle \frac{2\cancel{\left(x-1\right)}\cdot 8}{\cancel{x-1}}=}$${\displaystyle 16}$;

4) ${\displaystyle (3a+1):\frac{3+9a}{2}=}$${\displaystyle (3a+1)\cdot \frac{2}{3\left(1+3a\right)}=}$${\displaystyle \frac{\cancel{\left(3a+1\right)}\cdot 2}{3\cancel{\left(3a+1\right)}}=}$${\displaystyle \frac{2}{3}}$;

5) ${\displaystyle (ax+2a):\frac{x+2}{2a}=}$${\displaystyle a(x+2)\cdot \frac{2a}{x+2}=}$${\displaystyle \frac{a\cancel{\left(x+2\right)}\cdot 2a}{\cancel{x+2}}=}$${\displaystyle 2a^2}$;

6) ${\displaystyle (3b-ab):\frac{2a-6}{2b}=}$${\displaystyle b(3-a)\cdot \frac{2b}{2\left(a-3\right)}=}$${\displaystyle \frac{-b\cancel{\left(a-3\right)}\cdot \stackrel{1}{\cancel{2}}b}{\underset{1}{\cancel{2}}\cancel{\left(a-3\right)}}=}$${\displaystyle -b^2}$.