Упр.37.8 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (4x-y)/(x^2-y^2 )+1/(x-y);
2) y^2/(y^2-81)-y/(y+9);
3) 10a/(25a^2-9)-1/(5a+3);
4) n/(n-7)-n^2/(n^2-14n+49).

1. $$\frac{4x-y}{x^2-y^2}+\frac{1}{x-y}=\frac{4x-y}{(x-y)(x+y)}+\frac{x+y}{(x-y)(x+y)}$$
   $$=\frac{4x-y+x+y}{(x-y)(x+y)}=\frac{5x}{x^2-y^2}.$$
2. $$\frac{y^2}{y^2-81}-\frac{y}{y+9}=\frac{y^2}{(y-9)(y+9)}-\frac{y(y-9)}{(y-9)(y+9)}$$
   $$=\frac{y^2-y(y-9)}{y^2-81}=\frac{9y}{y^2-81}.$$
3. $$\frac{10a}{25a^2-9}-\frac{1}{5a+3}=\frac{10a}{(5a-3)(5a+3)}-\frac{5a-3}{(5a-3)(5a+3)}$$
   $$=\frac{10a-(5a-3)}{(5a-3)(5a+3)}=\frac{5a+3}{(5a-3)(5a+3)}=\frac{1}{5a-3}.$$
4. $$\frac{n}{n-7}-\frac{n^2}{n^2-14n+49}=\frac{n}{n-7}-\frac{n^2}{(n-7)^2}$$
   $$=\frac{n(n-7)-n^2}{(n-7)^2}=\frac{n^2-7n-n^2}{(n-7)^2}=-\frac{7n}{(n-7)^2}.$$

Ответ

1) $$\frac{5x}{x^2-y^2}$$
2) $$\frac{9y}{y^2-81}$$
3) $$\frac{1}{5a-3}$$
4) $$-\frac{7n}{(n-7)^2}$$