Упр.104 ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) a/(a-2) — (3a+1)/(3a-6);
2) 18/(b2+3b) — 6/b; Упростите выражение:
1) 1/(b(a-b)) — 1/(a(a-b));
2) 5/a + 30/(a(a-6));
3) 3/(x-2) — (2x+2)/(x(x-2));

1. $$\frac{a}{a-2}-\frac{3a+1}{3a-6}=\frac{a}{a-2}-\frac{3a+1}{3(a-2)}$$
   $$=\frac{3a-(3a+1)}{3(a-2)}=\frac{-1}{3(a-2)}$$

2. $$\frac{18}{b^2+3b}-\frac{6}{b}=\frac{18}{b(b+3)}-\frac{6(b+3)}{b(b+3)}$$
   $$=\frac{18-6b-18}{b(b+3)}=\frac{-6b}{b(b+3)}=-\frac{6}{b+3}$$

3. $$\frac{1}{b(a-b)}-\frac{1}{a(a-b)}=\frac{a-b}{ab(a-b)}=\frac{1}{ab}$$

4. $$\frac{5}{a}+\frac{30}{a(a-6)}=\frac{5(a-6)}{a(a-6)}+\frac{30}{a(a-6)}$$
   $$=\frac{5a-30+30}{a(a-6)}=\frac{5a}{a(a-6)}=\frac{5}{a-6}$$

5. $$\frac{3}{x-2}-\frac{2x+2}{x(x-2)}=\frac{3x-(2x+2)}{x(x-2)}$$
   $$=\frac{x-2}{x(x-2)}=\frac{1}{x}$$

Ответ

$$1)\ -\frac{1}{3(a-2)};\quad 2)\ -\frac{6}{b+3};\quad 3)\ \frac{1}{ab};\quad 4)\ \frac{5}{a-6};\quad 5)\ \frac{1}{x}.$$