185° Вправа 185Алгебра 8 клас Тарасенкова 2025 · § 5 · стор. 56

185. Знайдіть добуток дробів.

Спершу розкладаємо чисельники і знаменники на:

1) ${\displaystyle \frac{x+1}{3}\cdot \frac{6}{{(x+1)}^2}=}$${\displaystyle \frac{\cancel{\left(x+1\right)}\cdot 2\cdot \stackrel{1}{\cancel{3}}}{\underset{1}{\cancel{3}}\cancel{\left(x+1\right)}(x+1)}=}$${\displaystyle \frac{2}{x+1}}$;

2) ${\displaystyle \frac{5y-5}{7}\cdot \frac{21}{y-1}=}$${\displaystyle \frac{5\cancel{\left(y-1\right)}\cdot 3\cdot \stackrel{1}{\cancel{7}}}{\underset{1}{\cancel{7}}\cancel{\left(y-1\right)}}=}$${\displaystyle 15}$;

3) ${\displaystyle \frac{2a+1}{8}\cdot \frac{16}{2+4a}=}$${\displaystyle \frac{\cancel{\left(2a+1\right)}\cdot 2\cdot \stackrel{1}{\cancel{8}}}{\underset{2}{\cancel{16}}\cancel{\left(2a+1\right)}}=}$${\displaystyle 1}$;

4) ${\displaystyle \frac{1-b}{5}\cdot \frac{20}{{(b-1)}^2}=}$${\displaystyle \frac{\cancel{\left(1-b\right)}\cdot 4\cdot \stackrel{1}{\cancel{5}}}{\underset{1}{\cancel{5}}\cancel{\left(1-b\right)}(1-b)}=}$${\displaystyle \frac{4}{1-b}}$;

5) ${\displaystyle \frac{3-6y}{14}\cdot \frac{35}{2y-1}=}$${\displaystyle \frac{-3\cancel{\left(2y-1\right)}\cdot 5\cdot \stackrel{1}{\cancel{7}}}{2\cdot \underset{1}{\cancel{7}}\cancel{\left(2y-1\right)}}=}$${\displaystyle -\frac{15}{2}=}$${\displaystyle -7,5}$;

6) ${\displaystyle \frac{1-3x}{12}\cdot \frac{16}{6x-2}=}$${\displaystyle \frac{-\cancel{\left(3x-1\right)}\cdot 4\cdot \cancel{4}}{3\cdot \cancel{4}\cdot 2\cancel{\left(3x-1\right)}}=}$${\displaystyle -\frac{2}{3}}$.

(У пункті 4) ${\displaystyle {(b-1)}^2=}$${\displaystyle {(1-b)}^2}$.)