№ 6.8 Алгебра = № 11.8 Математика
Виконайте ділення:
1. $\frac{x-y}{2a^2}:\frac{y-x}{8a};$
2. $\frac{p^2+2p}{18a^2}:\frac{7p}{9a};$
3. $\frac{x^2+x}{9ab}:\frac{5x+5}{18a^2b};$
4. $\frac{3x-x^2}{7p}:\frac{2x-6}{14p^2}.$
Розв'язок:
1. $\frac{x-y}{2a^2}:\frac{y-x}{8a}=\frac{\left(x-y\right)\cdot8a}{-2a^2\cdot\left(x-y\right)}=-\frac{4}{a};$
2. $\frac{p^2+2p}{18a^2}:\frac{7p}{9a}=\frac{p\left(p+2\right)\cdot9a}{18a^2\cdot7p}=\frac{p+2}{14a};$
3. $\frac{x^2+x}{9ab}:\frac{5x+5}{18a^2b}=\frac{x\left(x+1\right)\cdot18a^2b}{9ab\cdot5\left(x+1\right)}=$
$= \frac{2xa}{5};$
4. $\frac{3x-x^2}{7p}:\frac{2x-6}{14p^2}=\frac{x\left(3-x\right)\cdot14p^2}{-7p\cdot2\left(3-x\right)}=$
$= \frac{-xp}{1}=-xp.$