Страница 71 номер 281, ГДЗ по алгебре за 9 класс к учебнику Мерзляка
Сократите дробь: 1) \(\frac{x^2 + x - 6}{7x + 21}\); 2) \(\frac{2y - 16}{8 + 7y - y^2}\); 3) \(\frac{m^2 - 16m + 63}{m^2 - 81}\); 4) \(\frac{3a^2 + a - 2}{4 - 9a^2}\).
1)
\(\dfrac{x^{2} + x - 6}{7x + 21} = \dfrac{(x - 2)(x + 3)}{7(x + 3)} = \dfrac{x - 2}{7}\)
2)
\(\dfrac{2y - 16}{8 + 7y - y^{2}} = \dfrac{2(y - 8)}{- (y^{2} - 7y - 8)} = \dfrac{2(y - 8)}{- (y + 1)(y - 8)} = - \dfrac{2}{y + 1}\)
3)
\(\dfrac{m^{2} - 16m + 63}{m^{2} - 81} = \dfrac{(m - 7)(m - 9)}{(m - 9)(m + 9)} = \dfrac{m - 7}{m + 9}\)
4) \(3a^{2} + a - 2 = 3(a + 1)\left( a - \frac{2}{3} \right) = (a + 1)(3a - 2)\)
\(D = 1 + 4 \cdot 3 \cdot 2 = 25\)
\(a_{1} = \dfrac{- 1 - 5}{6} = - 1;\ a_{2} = \dfrac{- 1 + 5}{6} = \dfrac{4}{6} = \dfrac{2}{3}\)
\(\dfrac{3a^{2} + a - 2}{4 - 9a^{2}} = \dfrac{(a + 1)(3a - 2)}{- \left( 9a^{2} - 4 \right)} =\)
\(= \dfrac{(a + 1)(3a - 2)}{- (3a - 2)(3a + 2)} = - \dfrac{a + 1}{3a + 2}\)
Ответ: 1) \(\frac{x - 2}{7}\); 2) \(- \frac{2}{y + 1}\); 3) \(\frac{m - 7}{m + 9}\); 4) \(- \frac{a + 1}{3a + 2}\).
