ЗПЗ §§ 5–8 Алгебра = ЗПЗ §§ 10–13 Математика
Виконайте дії:
1. $\frac{2a^3}{15m^2}\cdot\left(-\frac{5m}{6a^3}\right);$
2. $\frac{x^2-xy}{a^2}\cdot\frac{ab}{x^2-2xy+y^2};$
3. $-\frac{3m^2}{7c^3}:\left(-\frac{9m^3}{28c}\right);$
4. $\frac{x^2-16}{3x-6}:\frac{2x+8}{5x-10}.$
Розв'язок:
1. $\frac{2a^3}{15m^2}\cdot\left(-\frac{5m}{6a^3}\right)=-\frac{2a^3\cdot5m}{15m^2\cdot6a^3}=$
$= -\frac{1}{3m\cdot3}=-\frac{1}{9m};$
2. $\frac{x^2-xy}{a^2}\cdot\frac{ab}{x^2-2xy+y^2}=$
$= \frac{x\left(x-y\right)\cdot a b}{a\left(x-y\right)^2}=\frac{xb}{x-y};$
3. $-\frac{3m^2}{7c^3}:\left(-\frac{9m^3}{28c}\right)=$
$= \frac{3m^2}{7c^3}\cdot\frac{28c}{9m^3}=$
$= \frac{4}{3c^2m};$
4. $\frac{x^2-16}{3x-6}:\frac{2x+8}{5x-10}=$
$= \frac{x^2-16}{3x-6}\cdot\frac{5x-10}{2x+8}=$
$= \frac{\left(x-4\right)\left(x+4\right)\cdot5\left(x-2\right)}{3\left(x-2\right)\cdot2\left(x+4\right)}=$
$= \frac{5\left(x-4\right)}{6}.$