Упр.36.5 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (a+b)/(c-7)+a/(7-c);
2) (2x-4y)/(x-3y)-(4x-14y)/(3y-x);
3) (81b^2)/(9b-a)+a^2/(a-9b);
4) y^2/(y-1)-(1-2y)/(1-y).

1. $$\frac{a+b}{c-7}+\frac{a}{7-c}=\frac{a+b}{c-7}-\frac{a}{c-7}=\frac{a+b-a}{c-7}=\frac{b}{c-7}.$$
2. $$\frac{2x-4y}{x-3y}-\frac{4x-14y}{3y-x}=\frac{2x-4y}{x-3y}+\frac{4x-14y}{x-3y}$$
   $$=\frac{2x-4y+4x-14y}{x-3y}=\frac{6x-18y}{x-3y}=\frac{6(x-3y)}{x-3y}=6.$$
3. $$\frac{81b^2}{9b-a}+\frac{a^2}{a-9b}=\frac{81b^2}{9b-a}-\frac{a^2}{9b-a}$$
   $$=\frac{81b^2-a^2}{9b-a}=\frac{(9b-a)(9b+a)}{9b-a}=9b+a.$$
4. $$\frac{y^2}{y-1}-\frac{1-2y}{1-y}=\frac{y^2}{y-1}+\frac{1-2y}{y-1}$$
   $$=\frac{y^2+1-2y}{y-1}=\frac{(y-1)^2}{y-1}=y-1.$$

Ответ

1) $$\frac{b}{c-7}$$; 2) $$6$$; 3) $$9b+a$$; 4) $$y-1$$.