Упр.25 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

Выполните действия:

• 1) $$\frac{x+4}{2x-6}-\frac{x+1}{x-3}$$;
• 4) $$\frac{4b}{3b-21}+\frac{3b}{14-2b}$$;
• 2) $$\frac{a+3}{3a-3}+\frac{2-a}{5a-5}$$;
• 5) $$\frac{3p}{3p+2q}-\frac{9p^2}{9p^2+12pq+4q^2}$$;
• 3) $$\frac{x+5}{x-5}-\frac{x-1}{x+5}$$;
• 6) $$\frac{4}{c^2-36}-\frac{2}{c^2-6c}$$.

1) $$\frac{x+4}{2x-6}-\frac{x+1}{x-3}=\frac{x+4}{2(x-3)}-\frac{x+1}{x-3}=\frac{x+4-2(x+1)}{2(x-3)}=\frac{2-x}{2(x-3)}.$$

2) $$\frac{a+3}{3a-3}+\frac{2-a}{5a-5}=\frac{a+3}{3(a-1)}+\frac{2-a}{5(a-1)}=\frac{5(a+3)+3(2-a)}{15(a-1)}=\frac{2a+21}{15(a-1)}.$$

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

$$=\frac{x^2+10x+25-(x^2-6x+5)}{x^2-25}=\frac{16x+20}{x^2-25}.$$

4) $$\frac{4b}{3b-21}+\frac{3b}{14-2b}=\frac{4b}{3(b-7)}-\frac{3b}{2(b-7)}=\frac{8b-9b}{6(b-7)}=\frac{-b}{6(b-7)}=\frac{b}{6(7-b)}.$$

5) $$\frac{3p}{3p+2q}-\frac{9p^2}{9p^2+12pq+4q^2}=\frac{3p}{3p+2q}-\frac{9p^2}{(3p+2q)^2}$$

$$=\frac{3p(3p+2q)-9p^2}{(3p+2q)^2}=\frac{9p^2+6pq-9p^2}{(3p+2q)^2}=\frac{6pq}{(3p+2q)^2}.$$

6) $$\frac{4}{c^2-36}-\frac{2}{c^2-6c}=\frac{4}{(c-6)(c+6)}-\frac{2}{c(c-6)}$$

$$=\frac{4c-2(c+6)}{c(c-6)(c+6)}=\frac{2c-12}{c(c-6)(c+6)}=\frac{2(c-6)}{c(c-6)(c+6)}=\frac{2}{c(c+6)}.$$