Упр.35.4 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (2a+2b)/7(a+b) ;
2) (4(a-6)^2)/(a-6)^3 ;
3) (12a+18b)/12a;
4) (7x-21y)/(5x-15y);
5) (a-5b)/(a^2-5ab);
6) (c^2-6c+9)/(c^2-9);
7) (m^3+1)/(m^2-m+1);
8) (3x-6y)/(4y-2x);
9) (m^2-5mn)/(15n-3m);
10) (7a^4-a^3 b)/(b^4-7ab^3 );
11) (x^2-25)/(5x^2-x^3 );
12) (y^2-12y+36)/(36-y^2 ).

1. $$\frac{2a+2b}{7(a+b)}=\frac{2(a+b)}{7(a+b)}=\frac{2}{7}.$$
2. $$\frac{4(a-6)^2}{(a-6)^3}=\frac{4}{a-6}.$$
3. $$\frac{12a+18b}{12a}=\frac{6(2a+3b)}{12a}=\frac{2a+3b}{2a}.$$
4. $$\frac{7x-21y}{5x-15y}=\frac{7(x-3y)}{5(x-3y)}=\frac{7}{5}.$$
5. $$\frac{a-5b}{a^2-5ab}=\frac{a-5b}{a(a-5b)}=\frac{1}{a}.$$
6. $$\frac{c^2-6c+9}{c^2-9}=\frac{(c-3)^2}{(c-3)(c+3)}=\frac{c-3}{c+3}.$$
7. $$\frac{m^3+1}{m^2-m+1}=\frac{(m+1)(m^2-m+1)}{m^2-m+1}=m+1.$$
8. $$\frac{3x-6y}{4y-2x}=\frac{3(x-2y)}{-2(x-2y)}=-\frac{3}{2}.$$
9. $$\frac{m^2-5mn}{15n-3m}=\frac{m(m-5n)}{-3(m-5n)}=-\frac{m}{3}.$$
10. $$\frac{7a^4-a^3b}{b^4-7ab^3}=\frac{a^3(7a-b)}{-b^3(7a-b)}=-\frac{a^3}{b^3}.$$
11. $$\frac{x^2-25}{5x^2-x^3}=\frac{(x-5)(x+5)}{-x^2(x-5)}=-\frac{x+5}{x^2}.$$
12. $$\frac{y^2-12y+36}{36-y^2}=\frac{(y-6)^2}{(6-y)(6+y)}=\frac{6-y}{6+y}.$$

Ответ

1. $$\frac{2}{7}$$
2. $$\frac{4}{a-6}$$
3. $$\frac{2a+3b}{2a}$$
4. $$\frac{7}{5}$$
5. $$\frac{1}{a}$$
6. $$\frac{c-3}{c+3}$$
7. $$m+1$$
8. $$-\frac{3}{2}$$
9. $$-\frac{m}{3}$$
10. $$-\frac{a^3}{b^3}$$
11. $$-\frac{x+5}{x^2}$$
12. $$\frac{6-y}{6+y}$$