№ 6.7 Алгебра = № 11.7 Математика
Виконайте ділення:
1. $\frac{2a+b}{4p}:\frac{b+2a}{8p^2};$
2. $\frac{3a-2x}{7x^2}:\frac{2x-3a}{14x};$
3. $\frac{a^2-3a}{9y^2}:\frac{5a}{9y};$
4. $\frac{a^2+a}{9b^2}:\frac{5+5a}{b^3};$
5. $\frac{7ab}{c^2-3c}:\frac{14ab^2}{3c-9};$
6. $\frac{11a}{m^2-2m}:\frac{22a^2}{6-3m}.$
Розв'язок:
1. $\frac{2a+b}{4p}:\frac{b+2a}{8p^2}=\frac{\left(2a+b\right)\cdot8p^2}{4p\cdot\left(b+2a\right)}=$
$= \frac{2p}{1}=2p;$
2. $\frac{3a-2x}{7x^2}:\frac{2x-3a}{14x}=$
$= -\frac{14x\cdot\left(2x-3a\right)}{7x^2\cdot\left(2x-3a\right)}= -\frac{2}{x};$
3. $\frac{a^2-3a}{9y^2}:\frac{5a}{9y}=\frac{a\left(a-3\right)\cdot9y}{9y^2\cdot5a}=\frac{a-3}{5y};$
4. $\frac{a^2+a}{9b^2}:\frac{5+5a}{b^3}=\frac{a\left(a+1\right)\cdot b^3}{9b^2\cdot5\left(1+a\right)}=\frac{ab}{45};$
5. $\frac{7ab}{c^2-3c}:\frac{14ab^2}{3c-9}=\frac{7ab\cdot3\left(c-3\right)}{14ab^2\cdot c\left(c-3\right)}=$
$= \frac{3}{2bc};$
6. $\frac{11a}{m^2-2m}:\frac{22a^2}{6-3m}=\frac{11a\cdot3\left(2-m\right)}{22a^2\cdot m\left(m-2\right)}=$
$= -\frac{11a\cdot3\left(m-2\right)}{22a^2\cdot m\left(m-2\right)}=-\frac{3}{2am}.$