Упр.15.1 ГДЗ Мордкович Семенов 8 класс (Алгебра)

а) (6a^3 b)/c^2 · c/(3ab^2);
б) (12x^2 y^2)/c : (4xy^4)/c^2;
в) -(19x^2 y)/(25a^2) : (38xy^2)/45a;
г) 21ay/8bx · (-(12bx^2)/(35a^2 y));
д) (-(a^5 b)/(15c^2 )) · (-(20c^3)/(a^4 b^3));
е) (-ay/(10x^2)) : (-(2y^2)/(15ax^2)).

а) $$\frac{6a^3b}{c^2}\cdot\frac{c}{3ab^2}=\frac{6a^3bc}{3ab^2c^2}=\frac{2a^2}{bc}$$

б) $$\frac{12x^2y^2}{c}:\frac{4xy^4}{c^2}=\frac{12x^2y^2}{c}\cdot\frac{c^2}{4xy^4}=\frac{3xc}{y^2}$$

в) $$-\frac{19x^2y}{25a^2}:\frac{38xy^2}{45a}=-\frac{19x^2y}{25a^2}\cdot\frac{45a}{38xy^2}=-\frac{9x}{10ay}$$

г) $$\frac{21ay}{8bx}\cdot\left(-\frac{12bx^2}{35a^2y}\right)=-\frac{21ay\cdot12bx^2}{8bx\cdot35a^2y}=-\frac{9x}{10a}$$

д) $$-\frac{a^5b}{15c^2}\cdot\left(-\frac{20c^3}{a^4b^3}\right)=\frac{a^5b\cdot20c^3}{15c^2\cdot a^4b^3}=\frac{4ac}{3b^2}$$

е) $$-\frac{ay}{10x^2}:\left(-\frac{2y^2}{15ax^2}\right)=\frac{ay}{10x^2}\cdot\frac{15ax^2}{2y^2}=\frac{3a^2}{4y}$$

Ответ

а) $$\frac{2a^2}{bc}$$; б) $$\frac{3xc}{y^2}$$; в) $$-\frac{9x}{10ay}$$; г) $$-\frac{9x}{10a}$$; д) $$\frac{4ac}{3b^2}$$; е) $$\frac{3a^2}{4y}$$.