Упр.73 ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (5x+3)/(x2-16) + (6x-1)/(16-x2) при x = -4,1;
2) (a2+a)/(a2-9) — (7a-9)/(a2-9) при a = 7. Упростите выражение:
1) x/(y-1) + 2/(1-y);
2) 3c/(c-d) + 3d/(d-c);
3) (3m+2n)/(2m-3n) — (m-8n)/(3n-2m);
4) b2/(2b-14) + 49/(14-2b).

1. При $$x=-4{,}1$$:

   $$\frac{5x+3}{x^2-16}+\frac{6x-1}{16-x^2} =\frac{5x+3}{x^2-16}-\frac{6x-1}{x^2-16} =\frac{5x+3-6x+1}{x^2-16}$$

   $$=\frac{-x+4}{(x-4)(x+4)} =\frac{-(x-4)}{(x-4)(x+4)} =-\frac{1}{x+4}$$

   $$-\frac{1}{-4{,}1+4}=-\frac{1}{-0{,}1}=10.$$

2. При $$a=7$$:

   $$\frac{a^2+a}{a^2-9}-\frac{7a-9}{a^2-9} =\frac{a^2+a-7a+9}{a^2-9} =\frac{a^2-6a+9}{a^2-9}$$

   $$=\frac{(a-3)^2}{(a-3)(a+3)} =\frac{a-3}{a+3}$$

   $$\frac{7-3}{7+3}=\frac{4}{10}=0{,}4.$$

3. $$\frac{x}{y-1}+\frac{2}{1-y} =\frac{x}{y-1}-\frac{2}{y-1} =\frac{x-2}{y-1}.$$

4. $$\frac{3c}{c-d}+\frac{3d}{d-c} =\frac{3c}{c-d}-\frac{3d}{c-d} =\frac{3c-3d}{c-d} =\frac{3(c-d)}{c-d}=3.$$

5. $$\frac{3m+2n}{2m-3n}-\frac{m-8n}{3n-2m} =\frac{3m+2n}{2m-3n}+\frac{m-8n}{2m-3n}$$

   $$=\frac{3m+2n+m-8n}{2m-3n} =\frac{4m-6n}{2m-3n} =\frac{2(2m-3n)}{2m-3n}=2.$$

6. $$\frac{b^2}{2b-14}+\frac{49}{14-2b} =\frac{b^2}{2b-14}-\frac{49}{2b-14} =\frac{b^2-49}{2b-14}$$

   $$=\frac{(b-7)(b+7)}{2(b-7)} =\frac{b+7}{2}.$$

Ответ

1) $$10$$; 2) $$0{,}4$$; 3) $$\frac{x-2}{y-1}$$; 4) $$3$$; 5) $$2$$; 6) $$\frac{b+7}{2}$$.