Упр.38.7 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (x^2-y^2)/x^2 : (6x+6y)/x^5 ;
2) (c-5)/(c^2-4c) : (c-5)/(5c-20);
3) (x-y)/xy : (x^2-y^2)/3xy;
4) (a^2-4a+4)/(a+2) : (a-2);
5) (p^2-16k^2 ) : (p+4k)/p;
6) (a^2-ab)/a^2 : (a^2-2ab+b^2)/ab.

1. $$\frac{x^2-y^2}{x^2}:\frac{6x+6y}{x^5}=\frac{(x-y)(x+y)}{x^2}:\frac{6(x+y)}{x^5}$$
   $$=\frac{(x-y)(x+y)}{x^2}\cdot\frac{x^5}{6(x+y)}=\frac{x^3(x-y)}{6}$$
2. $$\frac{c-5}{c^2-4c}:\frac{c-5}{5c-20}=\frac{c-5}{c(c-4)}:\frac{c-5}{5(c-4)}$$
   $$=\frac{c-5}{c(c-4)}\cdot\frac{5(c-4)}{c-5}=\frac{5}{c}$$
3. $$\frac{x-y}{xy}:\frac{x^2-y^2}{3xy}=\frac{x-y}{xy}\cdot\frac{3xy}{x^2-y^2}$$
   $$=\frac{x-y}{xy}\cdot\frac{3xy}{(x-y)(x+y)}=\frac{3}{x+y}$$
4. $$\frac{a^2-4a+4}{a+2}:(a-2)=\frac{(a-2)^2}{a+2}\cdot\frac{1}{a-2}$$
   $$=\frac{a-2}{a+2}$$
5. $$\left(p^2-16k^2\right):\frac{p+4k}{p}=\left(p-4k\right)\left(p+4k\right)\cdot\frac{p}{p+4k}$$
   $$=p(p-4k)$$
6. $$\frac{a^2-ab}{a^2}:\frac{a^2-2ab+b^2}{ab}=\frac{a(a-b)}{a^2}:\frac{(a-b)^2}{ab}$$
   $$=\frac{a(a-b)}{a^2}\cdot\frac{ab}{(a-b)^2}=\frac{b}{a-b}$$

Ответ

1) $$\frac{x^3(x-y)}{6}$$; 2) $$\frac{5}{c}$$; 3) $$\frac{3}{x+y}$$; 4) $$\frac{a-2}{a+2}$$; 5) $$p(p-4k)$$; 6) $$\frac{b}{a-b}$$.