Упр.6.1 ГДЗ Мордкович 8 класс (Алгебра)

6.1 а) (c/2+c/3)*1/c2;
б) (2x/y2-1/2x):(1/y+1/2x);
в) d2/3*(d/2+2/d2);
г) (a/b2-1/a):(1/b+1/a).

1. $$\left(\frac{c}{2}+\frac{c}{3}\right)\cdot \frac{1}{c^2}=\left(\frac{3c+2c}{6}\right)\cdot \frac{1}{c^2}=\frac{5c}{6c^2}=\frac{5}{6c}.$$

2. $$\left(\frac{2x}{y^2}-\frac{1}{2x}\right):\left(\frac{1}{y}+\frac{1}{2x}\right)=\frac{4x^2-y^2}{2xy^2}:\frac{2x+y}{2xy}.$$

   $$\frac{4x^2-y^2}{2xy^2}\cdot \frac{2xy}{2x+y}=\frac{(2x-y)(2x+y)\cdot 2xy}{2xy^2(2x+y)}=\frac{2x-y}{y}.$$

3. $$\frac{d^2}{3}\cdot \left(\frac{d}{2}+\frac{2}{d^2}\right)=\frac{d^2}{3}\cdot \frac{d}{2}+\frac{d^2}{3}\cdot \frac{2}{d^2}=\frac{d^3}{6}+\frac{2}{3}=\frac{d^3+4}{6}.$$

4. $$\left(\frac{a}{b^2}-\frac{1}{a}\right):\left(\frac{1}{b}+\frac{1}{a}\right)=\frac{a^2-b^2}{ab^2}:\frac{a+b}{ab}.$$

   $$\frac{a^2-b^2}{ab^2}\cdot \frac{ab}{a+b}=\frac{(a-b)(a+b)\cdot ab}{ab^2(a+b)}=\frac{a-b}{b}.$$

Ответ

а) $$\frac{5}{6c}$$; б) $$\frac{2x-y}{y}$$; в) $$\frac{d^3+4}{6}$$; г) $$\frac{a-b}{b}$$.