Задание 2 Параграф 4 ГДЗ Рабочая тетрадь 1 Мерзляк Полонский 8 класс (Алгебра)

1) (a+6)/18+(a-3)/9;
2) (4n-1)/n-(4m-2)/m;
3) (6-c)/4p+(c-3)/6n;
4) (3b+2)/(ab^2 )-(3a-5)/(a^2 b);
5) 1/c^3 -(8+c^3)/c^6 ;
6) 5/m+(7m-5)/(m-2);
7) 9/x-9/(x+2);
8) b/(b-5)-5/(b+5);
9) y/(y+1)+4/(2y+1).

1. $$\frac{a+6}{18}+\frac{a-3}{9}=\frac{a+6}{18}+\frac{2(a-3)}{18}=\frac{a+6+2a-6}{18}=\frac{3a}{18}=\frac{a}{6}.$$
2. $$\frac{4n-1}{n}-\frac{4m-2}{m}=\frac{m(4n-1)-n(4m-2)}{mn}=\frac{4mn-m-4mn+2n}{mn}=\frac{2n-m}{mn}.$$
3. $$\frac{6-c}{4p}+\frac{c-3}{6n}=\frac{3n(6-c)+2p(c-3)}{12pn}=\frac{18n-3cn+2pc-6p}{12pn}.$$
4. $$\frac{3b+2}{ab^2}-\frac{3a-5}{a^2b}=\frac{a(3b+2)-b(3a-5)}{a^2b^2}=\frac{3ab+2a-3ab+5b}{a^2b^2}=\frac{2a+5b}{a^2b^2}.$$
5. $$\frac{1}{c^3}-\frac{8+c^3}{c^6}=\frac{c^3-(8+c^3)}{c^6}=\frac{c^3-8-c^3}{c^6}=-\frac{8}{c^6}.$$
6. $$\frac{5}{m}+\frac{7m-5}{m-2}=\frac{5(m-2)+m(7m-5)}{m(m-2)}=\frac{5m-10+7m^2-5m}{m(m-2)}=\frac{7m^2-10}{m(m-2)}.$$
7. $$\frac{9}{x}-\frac{9}{x+2}=\frac{9(x+2)-9x}{x(x+2)}=\frac{9x+18-9x}{x(x+2)}=\frac{18}{x(x+2)}.$$
8. $$\frac{b}{b-5}-\frac{5}{b+5}=\frac{b(b+5)-5(b-5)}{(b-5)(b+5)}=\frac{b^2+5b-5b+25}{b^2-25}=\frac{b^2+25}{b^2-25}.$$
9. $$\frac{y}{y+1}+\frac{4}{2y+1}=\frac{y(2y+1)+4(y+1)}{(y+1)(2y+1)}=\frac{2y^2+y+4y+4}{(y+1)(2y+1)}=\frac{2y^2+5y+4}{(y+1)(2y+1)}.$$

Ответ

1. $$\frac{a}{6}$$
2. $$\frac{2n-m}{mn}$$
3. $$\frac{18n-3cn+2pc-6p}{12pn}$$
4. $$\frac{2a+5b}{a^2b^2}$$
5. $$-\frac{8}{c^6}$$
6. $$\frac{7m^2-10}{m(m-2)}$$
7. $$\frac{18}{x(x+2)}$$
8. $$\frac{b^2+25}{b^2-25}$$
9. $$\frac{2y^2+5y+4}{(y+1)(2y+1)}$$