Упр.21 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (a-2)/(a-1)-a/(1-a);
2) (3y+7)/(4-y)+(y+15)/(y-4);
3) (2a-3)^2/(9a-27)+(a-6)^2/(27-9a);
4) (25-3x)/(x-5)^2 -(7x-x^2)/(5-x)^2.

1. $$\frac{a-2}{a-1}-\frac{a}{1-a}=\frac{a-2}{a-1}+\frac{a}{a-1}=\frac{a-2+a}{a-1}=\frac{2a-2}{a-1}=\frac{2(a-1)}{a-1}=2,$$
   $$a\ne 1.$$

2. $$\frac{3y+7}{4-y}+\frac{y+15}{y-4}=\frac{3y+7}{4-y}-\frac{y+15}{4-y}=\frac{3y+7-(y+15)}{4-y}$$
   $$=\frac{2y-8}{4-y}=\frac{2(y-4)}{4-y}=\frac{-2(4-y)}{4-y}=-2,$$
   $$y\ne 4.$$

3. $$\frac{(2a-3)^2}{9a-27}+\frac{(a-6)^2}{27-9a}=\frac{(2a-3)^2}{9a-27}-\frac{(a-6)^2}{9a-27}$$
   $$=\frac{4a^2-12a+9-(a^2-12a+36)}{9a-27}=\frac{3a^2-27}{9a-27}$$
   $$=\frac{3(a^2-9)}{9(a-3)}=\frac{3(a-3)(a+3)}{9(a-3)}=\frac{a+3}{3},$$
   $$a\ne 3.$$

4. $$\frac{25-3x}{(x-5)^2}-\frac{7x-x^2}{(5-x)^2}=\frac{25-3x-(7x-x^2)}{(x-5)^2}$$
   $$=\frac{x^2-10x+25}{(x-5)^2}=\frac{(x-5)^2}{(x-5)^2}=1,$$
   $$x\ne 5.$$

Ответ

1) $$2$$; 2) $$-2$$; 3) $$\frac{a+3}{3}$$; 4) $$1$$.