Упражнение 147

\(1)\ \frac{3a+b}{4c}\cdot\frac{c}{3a+b}=\frac{ (3a+b)\cdot{c}}{4c\cdot(3a+b)}=\frac{1\cdot1}{4\cdot1}=\frac{1}{4};\)

\(2)\ \frac{ab-b^2}{8}\cdot\frac{4a}{b^4}=\frac{ b(a-b)\cdot4a}{8\cdot{b}^4}=\frac{ (a-b)\cdot{a}}{2\cdot{b}^3}=\frac{a^2-ab}{2b^3};\)

\(3)\ \frac{5x-5y}{x^6}\cdot\frac{x^3}{x-y}=\frac{ 5(x-y)\cdot{x}^3}{x^6\cdot(x-y)}=\frac{5\cdot1}{x^3\cdot1}=\frac{5}{x^3};\)

\(4)\ \frac{18b}{b^2-16}\cdot\frac{b+4}{3b}=\frac{18b\cdot(b+4)}{ (b-4)(b+4)\cdot3b}=\frac{6\cdot1}{ (b-4)\cdot1}=\frac{6}{b-4};\)

\(5)\ \frac{6}{m^2-9n^2}\cdot(m-3n)=\frac{6}{m^2-9n^2}\cdot\frac{m-3n}{1}=\frac{6\cdot(m-3n)}{ (m-3n)(m+3n)}=\frac{6\cdot1}{m+3n}=\frac{6}{m+3n};\)

\(6)\ \frac{3c-9}{9c^2+6c+1}\cdot\frac{3c+1}{c-3}=\frac{ 3(c-3)\cdot(3c+1)}{ (3c+1)^2\cdot(c-3)}=\frac{3\cdot1}{ (3c+1)\cdot1}=\frac{3}{3c+1}.\)