Задание 525

Решение:

• \({\largeа)}\ \frac{a+1}{7x}\cdot\frac{2x}{a+1}=\frac{1}{7}\cdot\frac{2}{1}=\frac{2}{7}\)

• \({\largeб)}\ \frac{2m}{m-n}:\frac{3mn}{m-n}=\frac{2m}{m-n}\cdot\frac{m-n}{3mn}=\frac{2}{1}\cdot\frac{1}{3n}=\frac{2}{3n}\)

• \({\largeв)}\ \frac{4p}{p-3}\cdot\frac{p-3}{2p^2}=\frac{2}{1}\cdot\frac{1}{p}=\frac{2}{p}\)

• \({\largeг)}\ \frac{x+y}{8a}:\frac{x+y}{16a^2b}=\frac{x+y}{8a}\cdot\frac{16a^2b}{x+y}=\frac{1}{1}\cdot\frac{2ab}{1}=\frac{2ab}{1}=2ab\)

• \({\largeд)}\ \frac{2x+2y}{3}\cdot\frac{6}{x+y}=\frac{ 2(x+y)}{3}\cdot\frac{6}{x+y}=\frac{2}{1}\cdot\frac{2}{1}=\frac{4}{1}=4\)

• \({\largeе)}\ \frac{4a}{a^2b}:\frac{5ab}{3a-3b}=\frac{4a}{a^2b}\cdot\frac{3a-3b}{5ab}=\frac{4}{a^2b}\cdot\frac{3a-3b}{5b}=\frac{12a-12b}{5a^2b^2}\)

• \({\largeж)}\ \frac{m-3n}{6m}\cdot\frac{3mn}{4m-12n}=\frac{m-3n}{6m}\cdot\frac{3mn}{ 4(m-3n)}=\frac{1}{2}\cdot\frac{n}{4}=\frac{n}{8}\)

• \({\largeз)}\ \frac{2p-4q}{3p^2}:\frac{3p-6q}{4pq}=\frac{2p-4q}{3p^2}\cdot\frac{4pq}{3p-6q}=\frac{ 2(p-2q)}{3p^2}\cdot\frac{4pq}{ 3(p-2q)}=\frac{2}{3p}\cdot\frac{4q}{3}=\frac{8q}{9p}\)

• \({\largeи)}\ \frac{ax-ay}{cd}\cdot\frac{cx+cy}{x-y}=\frac{ a(x-y)}{cd}\cdot\frac{ c(x+y)}{x-y}=\frac{a}{d}\cdot\frac{x+y}{1}=\frac{ax+ay}{d}\)

• \({\largeк)}\ \frac{mk}{am-an}:\frac{ka-k}{2m-2n}=\frac{mk}{am-an}\cdot\frac{2m-2n}{ka-k}=\frac{mk}{ a(m-n)}\cdot\frac{ 2(m-n)}{ k(a-1)}=\frac{m}{a}\cdot\frac{2}{a-1}=\frac{2m}{a^2-a}\)