Упр.338 ГДЗ Муравин 7 класс (Алгебра)

1. Найдите значение дроби: 1) $$\frac{5a^3-10a^2}{(a-2)^2}$$ при $$a=1{,}8$$; 2) $$\frac{6(b-3)^2}{3b^3-9b^2}$$ при $$b=1{,}2$$; 3) $$\frac{2abc-ac^2}{2b^2-bc}$$ при $$a=-1\frac{2}{3}$$, $$b=\frac{1}{6}$$, $$c=\frac{1}{2}$$; 4) $$\frac{xy+2xz}{y^2z+2yz^2}$$ при $$x=\frac{1}{2}$$, $$y=-\frac{1}{6}$$, $$z=-\frac{1}{8}$$.

1. $$\frac{5a^3-10a^2}{(a-2)^2}=\frac{5a^2(a-2)}{(a-2)^2}=\frac{5a^2}{a-2}.$$
   При $$a=1{,}8$$:
   $$\frac{5\cdot 1{,}8^2}{1{,}8-2}=\frac{5\cdot 3{,}24}{-0{,}2}=\frac{16{,}2}{-0{,}2}=-81.$$

2. $$\frac{6(b-3)^2}{3b^3-9b^2}=\frac{6(b-3)^2}{3b^2(b-3)}=\frac{2(b-3)}{b^2}.$$
   При $$b=1{,}2$$:
   $$\frac{2(1{,}2-3)}{1{,}2^2}=\frac{2\cdot(-1{,}8)}{1{,}44}=\frac{-3{,}6}{1{,}44}=-2{,}5.$$

3. $$\frac{2abc-ac^2}{2b^2-bc}=\frac{ac(2b-c)}{b(2b-c)}=\frac{ac}{b}.$$
   При $$a=-1\frac{2}{3}=-\frac{5}{3},\ b=\frac{1}{6},\ c=\frac{1}{2}$$:
   $$\frac{ac}{b}=\frac{-\frac{5}{3}\cdot\frac{1}{2}}{\frac{1}{6}}=\frac{-\frac{5}{6}}{\frac{1}{6}}=-5.$$

4. $$\frac{xy+2xz}{y^2z+2yz^2}=\frac{x(y+2z)}{yz(y+2z)}=\frac{x}{yz}.$$
   При $$x=\frac{1}{2},\ y=-\frac{1}{6},\ z=-\frac{1}{8}$$:
   $$\frac{x}{yz}=\frac{\frac{1}{2}}{\left(-\frac{1}{6}\right)\left(-\frac{1}{8}\right)}=\frac{\frac{1}{2}}{\frac{1}{48}}=24.$$

Ответ

1) $$-81$$; 2) $$-2{,}5$$; 3) $$-5$$; 4) $$24$$.