№ 6.3 Алгебра = № 11.3 Математика
Спростіть вираз:
1. $\frac{7b}{12a}:\frac{21b^2}{16a};$
2. $\frac{15}{2n^2}:\frac{3m}{8n};$
3. $\frac{9b}{14a}:\frac{5b^2}{21a^2};$
4. $-\frac{3x^2}{a}:\frac{6x^3}{a^2};$
5. $ 14x^2:\frac{7x}{a};$
6. $\frac{8x^3}{7a}:\left(-2x^2\right);$
7. $-\frac{12a^2}{b}:\left(16a^2\right);$
8. $-40ma^5:\left(-\frac{8m^2}{a}\right).$
Розв'язок:
1. $\frac{7b}{12a}:\frac{21b^2}{16a}=\frac{7b\cdot16a}{12a\cdot21b^2}=\frac{4}{9b};$
2. $\frac{15}{2n^2}:\frac{3m}{8n}=\frac{15\cdot8n}{2n^2\cdot3m}=\frac{20}{nm};$
3. $\frac{9b}{14a}:\frac{5b^2}{21a^2}=\frac{9b\cdot21a^2}{14a\cdot5b^2}=\frac{27a}{10b};$
4. $-\frac{3x^2}{a}:\frac{6x^3}{a^2}=-\frac{3{x^2\cdot a}^2}{a\cdot6x^3}=-\frac{a}{2x};$
5. $ 14x^2:\frac{7x}{a}=\frac{14x^2\cdot a}{7x}=$
$= \frac{2xa}{1}=2xa;$
6. $\frac{8x^3}{7a}:\left(-2x^2\right)=\frac{8x^3\cdot1}{7a\cdot\left(-2x^2\right)}=$
$= -\frac{4x}{7a};$
7. $-\frac{12a^2}{b}:\left(16a^2\right)=-\frac{12a^2\cdot1}{b\cdot16a^2}=$
$= -\frac{3}{4b};$
8. $-40ma^5:\left(-\frac{8m^2}{a}\right)=$
$= \frac{40ma^5\cdot a}{8m^2}= \frac{5a^6}{m}.$