Упр.1.37 ГДЗ Дорофеев Суворова 8 класс (Алгебра)
а) (x^3-y^3)/(x^2-y^2 );
б) (x^3-y^3)/(x-y)^2;
в) (x+y)^2/(x^3+y^3 );
г) (x^3+y^3)/(x^3-x^2 y+xy^2 );
д) (x^2-y^2)/((x-y)^2 (x+y)^2 );
е) ((x-y)^2 (x+y)^2)/(x^4-y^4 ).
$$\frac{x^3-y^3}{x^2-y^2}=\frac{(x-y)(x^2+xy+y^2)}{(x-y)(x+y)}=\frac{x^2+xy+y^2}{x+y}.$$
$$\frac{x^3-y^3}{(x-y)^2}=\frac{(x-y)(x^2+xy+y^2)}{(x-y)^2}=\frac{x^2+xy+y^2}{x-y}.$$
$$\frac{(x+y)^2}{x^3+y^3}=\frac{(x+y)^2}{(x+y)(x^2-xy+y^2)}=\frac{x+y}{x^2-xy+y^2}.$$
$$\frac{x^3+y^3}{x^3-x^2y+xy^2}=\frac{(x+y)(x^2-xy+y^2)}{x(x^2-xy+y^2)}=\frac{x+y}{x}.$$
$$\frac{x^2-y^2}{(x-y)^2(x+y)^2}=\frac{(x-y)(x+y)}{(x-y)^2(x+y)^2}=\frac{1}{(x-y)(x+y)}=\frac{1}{x^2-y^2}.$$
$$\frac{(x-y)^2(x+y)^2}{x^4-y^4}=\frac{(x-y)^2(x+y)^2}{(x^2-y^2)(x^2+y^2)}=\frac{(x-y)^2(x+y)^2}{(x-y)(x+y)(x^2+y^2)}=\frac{(x-y)(x+y)}{x^2+y^2}=\frac{x^2-y^2}{x^2+y^2}.$$
Ответ
а) $$\frac{x^2+xy+y^2}{x+y}$$; б) $$\frac{x^2+xy+y^2}{x-y}$$; в) $$\frac{x+y}{x^2-xy+y^2}$$; г) $$\frac{x+y}{x}$$; д) $$\frac{1}{x^2-y^2}$$; е) $$\frac{x^2-y^2}{x^2+y^2}$$.
