\(1)\ \frac{a-b}{3b}\cdot\frac{3}{a-b}=\frac{ (a-b)\cdot3}{3b\cdot(a-b)}=\frac{1\cdot1}{b\cdot1}=\frac{1}{b};\)
\(2)\ \frac{2mn+n^2}{6m}\cdot\frac{2m}{n}=\frac{ n(2m+n)\cdot2m}{6m\cdot{n}}=\frac{ (2m+n)\cdot1}{3\cdot1}=\frac{2m+n}{3};\)
\(3)\ \frac{7a+7b}{b^6}\cdot\frac{b^3}{a+b}=\frac{ 7(a+b)\cdot{b}^3}{b^6\cdot(a+b)}=\frac{7\cdot1}{b^3\cdot1}=\frac{7}{b^3};\)
\(4)\ \frac{32a}{a^2-9}\cdot\frac{a-3}{8a}=\frac{32a\cdot(a-3)}{ (a-3)(a+3)\cdot8a}=\frac{4\cdot1}{ (a+3)\cdot1}=\frac{4}{a+3};\)
\(5)\ \frac{c-1}{c+6}\cdot\frac{c+6}{c^2-2c+1}=\frac{ (c-1)(c+6)}{ (c+6)(c-1)^2}=\frac{1\cdot1}{1\cdot(c-1)}=\frac{1}{c-1};\)
\(6)\ \frac{m-2}{m^2-49}\cdot\frac{m+7}{m-2}=\frac{ (m-2)(m+7)}{ (m-7)(m+7)(m-2)}=\frac{1\cdot1}{ (m-7)\cdot1}=\frac{1}{m-7};\)
\(7)\ (a+4)\cdot\frac{a}{2a+8}=\frac{a+4}{1}\cdot\frac{a}{2a+8}=\frac{ (a+4)\cdot{a}}{ 2(a+4)}=\frac{1\cdot{a}}{2}=\frac{a}{2};\)
\(8)\ \frac{x-9}{4x+8}\cdot\frac{x^2+2x}{x-9}=\frac{ (x-9)\cdot{x}(x+2)}{ 4(x+2)\cdot(x-9)}=\frac{1\cdot{x}}{4\cdot1}=\frac{x}{4};\)
\(9)\ \frac{4a^2-4a+1}{3a+3}\cdot\frac{a+1}{2a-1}=\frac{ (2a-1)^2\cdot(a+1)}{ 3(a+1)\cdot(2a-1)}=\frac{ (2a-1)\cdot1}{3\cdot1}=\frac{2a-1}{3};\)
\(10)\ \frac{a^2-25}{4a}\cdot\frac{4a^2}{a^2-5a}=\frac{ (a-5)(a+5)\cdot4a^2}{4a\cdot{a}(a-5)}=\frac{ (a+5)\cdot1}{1\cdot1}=a+5.\)
