Упр.526 ГДЗ Никольский Потапов 7 класс (Алгебра)
- а) $$\frac{a^2-b^2}{2a^2b}\cdot\frac{4ab^2}{a+b}$$; б) $$\frac{(x-y)^2}{3x^2y^3}:\frac{x-y}{6xy^2}$$; в) $$\frac{mn-m^2}{2m}\cdot\frac{8n}{n^2-m^2}$$; г) $$\frac{2a-4}{b+1}:\frac{a^2-4}{(b+1)^2}$$; д) $$\frac{x+y}{x-y}\cdot\frac{x^2-xy}{2x^2-2y^2}$$; е) $$\frac{16-m^2}{m^2-3m}:\frac{m^2+4m}{m^2-9}$$.
а)
$$\frac{a^2-b^2}{2a^2b}\cdot\frac{4ab^2}{a+b} =\frac{(a-b)(a+b)}{2a^2b}\cdot\frac{4ab^2}{a+b} =\frac{2b(a-b)}{a}.$$
б)
$$\frac{(x-y)^2}{3x^2y^3}:\frac{x-y}{6xy^2} =\frac{(x-y)^2}{3x^2y^3}\cdot\frac{6xy^2}{x-y} =\frac{2(x-y)}{xy}.$$
в)
$$\frac{mn-m^2}{2m}\cdot\frac{8n}{n^2-m^2} =\frac{m(n-m)}{2m}\cdot\frac{8n}{(n-m)(n+m)} =\frac{4n}{n+m}.$$
г)
$$\frac{2a-4}{b+1}:\frac{a^2-4}{(b+1)^2} =\frac{2(a-2)}{b+1}\cdot\frac{(b+1)^2}{(a-2)(a+2)} =\frac{2(b+1)}{a+2}.$$
д)
$$\frac{x+y}{x-y}\cdot\frac{x^2-xy}{2x^2-2y^2} =\frac{x+y}{x-y}\cdot\frac{x(x-y)}{2(x-y)(x+y)} =\frac{x}{2(x-y)}.$$
е)
$$\frac{16-m^2}{m^2-3m}:\frac{m^2+4m}{m^2-9} =\frac{(4-m)(4+m)}{m(m-3)}\cdot\frac{(m-3)(m+3)}{m(m+4)} =\frac{(4-m)(m+3)}{m^2}.$$
Ответ
а) $$\frac{2b(a-b)}{a}$$; б) $$\frac{2(x-y)}{xy}$$; в) $$\frac{4n}{n+m}$$; г) $$\frac{2(b+1)}{a+2}$$; д) $$\frac{x}{2(x-y)}$$; е) $$\frac{(4-m)(m+3)}{m^2}$$.
