Страница 204 номер 578, ГДЗ по алгебре за 9 класс к учебнику Алимова с ответами и решением
Упростить выражение (578—582). 1) \(\frac{a^5}{6c^3} : \frac{a^2}{4c^3}\); 2) \(\frac{9a^2}{m^3} : \frac{6a^2}{m^5}\); 3) \(\left(\frac{4a}{b^3}\right)^2 \cdot \frac{b^4}{8a}\); 4) \(\left(\frac{3c}{k^2}\right)^3 : \frac{9c}{k^3}\); 5) \(\frac{5a}{28b^2} \cdot 8ab \cdot \frac{7b}{5a^3}\); 6) \(\left(-\frac{25a^4b^3}{14c^2}\right) \cdot \left(\frac{-21c}{10a^3b^3}\right)\); 7) \(\frac{4x(x - 1) + 1}{4 - x^2} : \frac{1 - 2x}{x - 2}\); 8) \(\frac{x^2 - 4(x - 1)}{x - 1} : \frac{2 - x}{1 - x^2}\).
1) \(\frac{a^{5}}{6c^{3}} : \frac{a^{2}}{4c^{3}} = \frac{a^{5}}{6c^{3}} \cdot \frac{4c^{3}}{a^{2}} = \frac{2a^{3}}{3}\);
2) \(\frac{9a^{2}}{m^{3}} : \frac{6a^{2}}{m^{5}} = \frac{9a^{2}}{m^{3}} \cdot \frac{m^{5}}{6a^{2}} = \frac{3m^{2}}{2}\);
3) \(\left(\frac{4a}{b^{3}}\right)^{2} \cdot \frac{b^{4}}{8a} = \frac{16a^{2}}{b^{6}} \cdot \frac{b^{4}}{8a} = \frac{2a}{b^{2}}\);
4) \(\left(\frac{3c}{k^{2}}\right)^{3} : \frac{9c}{k^{3}} = \frac{27c^{3}}{k^{6}} \cdot \frac{k^{3}}{9c} = \frac{3c^{2}}{k^{3}}\);
5) \(\frac{5a}{28b^{2}} \cdot 8ab \cdot \frac{7b}{5a^{3}} = \frac{5 \cdot 8 \cdot 7 \cdot a^{2}b^{2}}{4 \cdot 7 \cdot 5 \cdot a^{3}b^{2}} = \frac{2}{a}\);
6) \(\left(-\frac{25a^{4}b^{3}}{14c^{2}}\right) \cdot \left(-\frac{21c}{10a^{3}b^{3}}\right) = \frac{5 \cdot 5 \cdot 3 \cdot 7 \cdot a^{4}b^{3}c}{2 \cdot 7 \cdot 2 \cdot 5 \cdot a^{3}b^{3}c^{2}} = \frac{15a}{4c}\);
7) \(\frac{4x(x - 1) + 1}{4 - x^{2}} : \frac{1 - 2x}{x - 2} = \frac{4x^{2} - 4x + 1}{(2 - x)(2 + x)} \cdot \frac{x - 2}{1 - 2x} = \frac{(2x - 1)^{2}}{(2 - x)(2 + x)} \cdot \frac{2 - x}{2x - 1} = \frac{2x - 1}{2 + x}\);
8) \(\frac{x^{2} - 4(x - 1)}{x - 1} : \frac{2 - x}{1 - x^{2}} = \frac{x^{2} - 4x + 4}{x - 1} \cdot \frac{(1 - x)(1 + x)}{2 - x} = \frac{(x - 2)^{2}}{x - 1} \cdot \frac{(x - 1)(x + 1)}{x - 2} =\)
\(= (x - 2)(x + 1).\)
