Задание 527

Решение:

• \({\largeа)}\ \frac{p^2-q^2}{p^2}\cdot\frac{pq+q^2}{ (p+q)^2}=\frac{ (p+q)(p-q)}{p^2}\cdot\frac{ q(p+q)}{ (p+q)^2}=\frac{p-q}{p^2}\cdot\frac{q}{1}=\frac{pq-q^2}{p^2}\)

• \({\largeб)}\ \frac{a^2-9b^2}{a^2-ab}:\frac{a^2+3ab}{a-b}=\frac{a^2-9b^2}{a^2-ab}\cdot\frac{a-b}{a^2+3ab}=\frac{ (a+3b)(a-3b)}{ a(a-b)}\cdot\frac{a-b}{ a(a+3b)}=\frac{a-3b}{a}\cdot\frac{1}{a}=\frac{a-3b}{a^2}\)

• \({\largeв)}\ \frac{3x^2-3y^2}{x^2+xy}\cdot\frac{x+y}{6x-6y}=\frac{ 3(x^2-y^2)}{ x(x+y)}\cdot\frac{x+y}{ 6(x-y)}=\frac{ 3(x+y)(x-y)}{ x(x+y)}\cdot\frac{x+y}{ 6(x-y)}=\frac{x+y}{x}\cdot\frac{1}{2}=\frac{x+y}{2x}\)

• \({\largeг)}\ \frac{m^2-n^2}{ (m+n)^2}:\frac{4m-4n}{3m+3n}=\frac{m^2-n^2}{ (m+n)^2}\cdot\frac{3m+3n}{4m-4n}=\frac{ (m+n)(m-n)}{ (m+n)^2}\cdot\frac{ 3(m+n)}{ 4(m-n)}=\frac{1}{1}\cdot\frac{3}{4}=\frac{3}{4}\)