Страница 93 номер 336, ГДЗ по алгебре за 9 класс к учебнику Мерзляка
Упростите выражение: 1) \(\frac{5a - 3}{8a} + \frac{a + 9}{4a}\); 2) \(\frac{5a - 6b}{ab} + \frac{5b - 5c}{bc}\); 3) \(\frac{8a + 5b}{5ab^2} - \frac{2a - 7b}{2a^2b}\); 4) \(\frac{m^2 + 4n^2}{8m^4n^4} - \frac{3m + 4n}{6m^5n^2}\).
1)
\(\dfrac{5a - 3}{8a} + \dfrac{a + 9}{4a} = \dfrac{5a - 3}{8a} + \dfrac{2(a + 9)}{2 \cdot 4a} =\)
\(= \dfrac{5a - 3 + 2a + 18}{8a} = \dfrac{7a + 15}{8a}\)
2)
\(\dfrac{5a - 6b}{ab} + \dfrac{5b - 5c}{bc} = \dfrac{(5a - 6b) \cdot c + (5b - 5c) \cdot a}{abc} =\)
\(= \dfrac{5ac - 6bc + 5ba - 5ca}{abc} = \dfrac{5ba - 6bc}{abc} = \dfrac{b(5a - 6c)}{abc} =\)
\(= \dfrac{5a - 6c}{ac}\)
3)
\(\dfrac{8a + 5b}{5ab^{2}} - \dfrac{2a - 7b}{2a^{2}b} = \dfrac{(8a + 5b) \cdot 2a - (2a - 7b) \cdot 5b}{10a^{2}b^{2}} =\)
\(= \dfrac{16a^{2} + 10ab - 10ab + 35b^{2}}{10a^{2}b^{2}} = \dfrac{16a^{2} + 35b^{2}}{10a^{2}b^{2}}\)
4)
\(\dfrac{m^{2} + 4n^{2}}{8m^{4}n^{4}} - \dfrac{3m + 4n}{6m^{5}n^{2}} = \dfrac{\left( m^{2} + 4n^{2} \right) \cdot 3m - (3m + 4n) \cdot 4n^{2}}{24m^{5}n^{4}} =\)
\(= \dfrac{3m^{3} + 12mn^{2} - 12mn^{2} - 16n^{3}}{24m^{5}n^{4}} = \dfrac{3m^{3} - 16n^{3}}{24m^{5}n^{4}}\)
Ответ: 1) \(\frac{7a + 15}{8a}\); 2) \(\frac{5a - 6c}{ac}\); 3) \(\frac{16a^{2} + 35b^{2}}{10a^{2}b^{2}}\); 4) \(\frac{3m^{3} - 16n^{3}}{24m^{5}n^{4}}\).
