Упражнение 151

\(1)\ \frac{a-b}{7a}:\frac{a-b}{7b}=\frac{a-b}{7a}\cdot\frac{7b}{a-b}=\frac{ (a-b)\cdot7b}{7a\cdot(a-b)}=\frac{1\cdot{b}}{a\cdot1}=\frac{b}{a};\)

\(2)\ \frac{x^2-y^2}{x^2}:\frac{6x+6y}{x^5}=\frac{x^2-y^2}{x^2}\cdot\frac{x^5}{6x+6y}=\frac{ (x-y)(x+y)\cdot{x}^5}{x^2\cdot6(x+y)}=\frac{ (x-y)\cdot{x}^3}{1\cdot6}=\frac{x^4-x^3y}{6};\)

\(3)\ \frac{c-5}{c^2-4c}:\frac{c-5}{5c-20}=\frac{c-5}{c^2-4c}\cdot\frac{5c-20}{c-5}=\frac{ (c-5)\cdot5(c-4)}{ c(c-4)\cdot(c-5)}=\frac{1\cdot5}{c\cdot1}=\frac{5}{c};\)

\(4)\ \frac{x-y}{xy}:\frac{x^2-y^2}{3xy}=\frac{x-y}{xy}\cdot\frac{3xy}{x^2-y^2}=\frac{ (x-y)\cdot3xy}{xy\cdot(x-y)(x+y)}=\frac{1\cdot3}{1\cdot(x+y)}=\frac{3}{x+y};\)

\(5)\ \frac{a^2-25}{a+7}:\frac{a-5}{a+7}=\frac{a^2-25}{a+7}\cdot\frac{a+7}{a-5}=\frac{ (a-5)(a+5)\cdot(a+7)}{ (a+7)\cdot(a-5)}=\frac{ (a+5)\cdot1}{1\cdot1}=a+5;\)

\(6)\ \frac{a^2-4a+4}{a+2}:(a-2)=\frac{a^2-4a+4}{a+2}:\frac{a-2}{1}=\frac{a^2-4a+4}{a+2}\cdot\frac{1}{a-2}=\frac{ (a-2)^2}{ (a+2)\cdot(a-2)}=\frac{a-2}{a+2};\)

\(7)\ (p^2-16k^2):\frac{p+4k}{p}=\frac{p^2-16k^2}{1}:\frac{p+4k}{p}=\frac{p^2-16k^2}{1}\cdot\frac{p}{p+4k}=\frac{ (p-4k)(p+4k)\cdot{p}}{p+4k}=\frac{ (p-4k)\cdot{p}}{1}=p^2-4kp;\)

\(8)\ \frac{a^2-ab}{a^2}:\frac{a^2-2ab+b^2}{ab}=\frac{a^2-ab}{a^2}\cdot\frac{ab}{a^2-2ab+b^2}=\frac{ a(a-b)\cdot{a}b}{a^2\cdot(a-b)^2}=\frac{1\cdot{b}}{1\cdot(a-b)}=\frac{b}{a-b}.\)