Упр.72 ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (a2-48)/(a-8) — 16/(a-8) при a=32;
2) (c2+3c+7)/(c3-8) + (c+3)/(8-c3) при c=-3. Выполните действия:
1) (a+b)/(c-7) + a/(7-c);
2) 5m/(m-n) + 5n/(n-m);
3) (2x-4y)/(x-3y) — (4x-14y)/(3y-x);

1. При $$a=32$$:

   $$\frac{a^2-48}{a-8}-\frac{16}{a-8}
   =\frac{a^2-48-16}{a-8}
   =\frac{a^2-64}{a-8}
   =\frac{(a-8)(a+8)}{a-8}
   =a+8=32+8=40.$$

2. При $$c=-3$$:

   $$\frac{c^2+3c+7}{c^3-8}+\frac{c+3}{8-c^3}
   =\frac{c^2+3c+7}{c^3-8}-\frac{c+3}{c^3-8}
   =\frac{c^2+2c+4}{c^3-8}.$$

   $$c^3-8=(c-2)(c^2+2c+4),$$
   значит
   $$\frac{c^2+2c+4}{c^3-8}=\frac{1}{c-2}.$$

   $$\frac{1}{c-2}=\frac{1}{-3-2}=-\frac{1}{5}.$$

3. $$\frac{a+b}{c-7}+\frac{a}{7-c}
   =\frac{a+b}{c-7}-\frac{a}{c-7}
   =\frac{a+b-a}{c-7}
   =\frac{b}{c-7}.$$

4. $$\frac{5m}{m-n}+\frac{5n}{n-m}
   =\frac{5m}{m-n}-\frac{5n}{m-n}
   =\frac{5m-5n}{m-n}
   =\frac{5(m-n)}{m-n}=5.$$

5. $$\frac{2x-4y}{x-3y}-\frac{4x-14y}{3y-x}
   =\frac{2x-4y}{x-3y}+\frac{4x-14y}{x-3y}$$
   $$=\frac{6x-18y}{x-3y}
   =\frac{6(x-3y)}{x-3y}=6.$$

Ответ

1) $$40$$; 2) $$-\frac{1}{5}$$; 3) $$\frac{b}{c-7}$$; 4) $$5$$; 5) $$6$$.