Упражнение 140

\({\largeа)}\ \frac{m^2-3m}{8x^2}:\frac{3m}{8x}=\frac{m^2-3m}{8x^2}\cdot\frac{8x}{3m}=\frac{ m(m-3)\cdot8x}{8x^2\cdot3m}=\frac{ (m-3)\cdot1}{x\cdot3}=\frac{m-3}{3x};\)

\({\largeб)}\ \frac{5a^2}{6b^3}:\frac{a^3}{ab-b^2}=\frac{5a^2}{6b^3}\cdot\frac{ab-b^2}{a^3}=\frac{5a^2\cdot{b}(a-b)}{6b^3\cdot{a^3}}=\frac{ 5\cdot(a-b)}{6b^2\cdot{a}}=\frac{5a-5b}{6ab^2};\)

\({\largeв)}\ \frac{x^2+x^3}{11a^2}:\frac{4+4x}{a^3}=\frac{x^2+x^3}{11a^2}\cdot\frac{a^3}{4+4x}=\frac{ x^2(1+x)\cdot{a^3}}{11a^2\cdot4(1+x)}=\frac{x^2\cdot{a}}{11\cdot4}=\frac{ax^2}{44};\)

\({\largeг)}\ \frac{6ax}{m^2-2m}:\frac{8ax}{3m-6}=\frac{6ax}{m^2-2m}\cdot\frac{3m-6}{8ax}=\frac{6ax\cdot3(m-2)}{ m(m-2)\cdot8ax}=\frac{3\cdot3}{m\cdot4}=\frac{9}{4m};\)

\({\largeд)}\ \frac{a^2-3ab}{3b}:(7a-21b)=\frac{a^2-3ab}{3b}:\frac{7a-21b}{1}=\frac{a^2-3ab}{3b}\cdot\frac{1}{7a-21b}=\frac{ a(a-3b)}{3b\cdot7(a-3b)}=\frac{a}{3b\cdot7}=\frac{a}{21b};\)

\({\largeе)}\ (x^2-4y^2):\frac{5x-10y}{x}=\frac{x^2-4y^2}{1}:\frac{5x-10y}{x}=\frac{x^2-4y^2}{1}\cdot\frac{x}{5x-10y}=\frac{ (x-2y)(x+2y)\cdot{x}}{ 5(x-2y)}=\frac{ (x+2y)\cdot{x}}{5}=\frac{x^2+2xy}{5};\)

\({\largeж)}\ (2a-b)^2:\frac{4a^3-ab^2}{3}=\frac{ (2a-b)^2}{1}:\frac{4a^3-ab^2}{3}=\frac{ (2a-b)^2}{1}\cdot\frac{3}{4a^3-ab^2}=\frac{ (2a-b)^2\cdot3}{ a(4a^2-b^2)}=\frac{ (2a-b)^2\cdot3}{ a(2a-b)(2a+b)}=\frac{ (2a-b)\cdot3}{ a(2a+b)}=\frac{6a-3b}{2a^2+ab};\)

\({\largeз)}\ (10m-15n):\frac{ (2m-3n)^2}{2m}=\frac{10m-15n}{1}:\frac{ (2m-3n)^2}{2m}=\frac{10m-15n}{1}\cdot\frac{2m}{ (2m-3n)^2}=\frac{ 5(2m-3n)\cdot2m}{ (2m-3n)^2}=\frac{5\cdot2m}{2m-3n}=\frac{10m}{2m-3n}.\)