118° Вправа 118Алгебра 8 клас Тарасенкова 2025 · § 3 · стор. 38

118. Зведіть дріб:

1) ${\displaystyle \frac{1}{ab}}$:

${\displaystyle \frac{1^{\mathrm{\setminus }2}}{ab}=}$${\displaystyle \frac{1\cdot 2}{ab\cdot 2}=}$${\displaystyle \frac{2}{2ab}}$;

${\displaystyle \frac{1^{\mathrm{\setminus }a}}{ab}=}$${\displaystyle \frac{1\cdot a}{ab\cdot a}=}$${\displaystyle \frac{a}{a^{2}b}}$;

${\displaystyle \frac{1^{\mathrm{\setminus }b}}{ab}=}$${\displaystyle \frac{1\cdot b}{ab\cdot b}=}$${\displaystyle \frac{b}{a{b}^2}}$;

${\displaystyle \frac{1^{\mathrm{\setminus }3a^2}}{ab}=}$${\displaystyle \frac{1\cdot 3a^2}{ab\cdot 3a^2}=}$${\displaystyle \frac{3a^2}{3a^{3}b}}$;

${\displaystyle \frac{1^{\mathrm{\setminus }-2ab}}{ab}=}$${\displaystyle \frac{1\cdot \left(-2ab\right)}{ab\cdot \left(-2ab\right)}=}$${\displaystyle \frac{-2ab}{-2a^2{b}^2}}$;

${\displaystyle \frac{1^{\mathrm{\setminus }3c}}{ab}=}$${\displaystyle \frac{1\cdot 3c}{ab\cdot 3c}=}$${\displaystyle \frac{3c}{3abc}}$;

2) ${\displaystyle \frac{x-y}{2xy}}$:

${\displaystyle \frac{{x-y}^{\mathrm{\setminus }2}}{2xy}=}$${\displaystyle \frac{(x-y)\cdot 2}{2xy\cdot 2}=}$${\displaystyle \frac{2x-2y}{4xy}}$;

${\displaystyle \frac{{x-y}^{\mathrm{\setminus }4x}}{2xy}=}$${\displaystyle \frac{(x-y)\cdot 4x}{2xy\cdot 4x}=}$${\displaystyle \frac{4x^2-4xy}{8x^{2}y}}$;

${\displaystyle \frac{{x-y}^{\mathrm{\setminus }3y}}{2xy}=}$${\displaystyle \frac{(x-y)\cdot 3y}{2xy\cdot 3y}=}$${\displaystyle \frac{3xy-3y^2}{6x{y}^2}}$;

${\displaystyle \frac{{x-y}^{\mathrm{\setminus }-6x^{2}y}}{2xy}=}$${\displaystyle \frac{(x-y)\cdot \left(-6x^{2}y\right)}{2xy\cdot \left(-6x^{2}y\right)}=}$${\displaystyle \frac{-6x^{3}y+6x^2{y}^2}{-12x^3{y}^2}}$;

${\displaystyle \frac{{x-y}^{\mathrm{\setminus }4a}}{2xy}=}$${\displaystyle \frac{(x-y)\cdot 4a}{2xy\cdot 4a}=}$${\displaystyle \frac{4ax-4ay}{8axy}}$;

3) ${\displaystyle \frac{2m-n}{m^{2}n}}$:

${\displaystyle \frac{{2m-n}^{\mathrm{\setminus }n}}{m^{2}n}=}$${\displaystyle \frac{(2m-n)\cdot n}{m^{2}n\cdot n}=}$${\displaystyle \frac{2mn-n^2}{m^2{n}^2}}$;

${\displaystyle \frac{{2m-n}^{\mathrm{\setminus }2m}}{m^{2}n}=}$${\displaystyle \frac{(2m-n)\cdot 2m}{m^{2}n\cdot 2m}=}$${\displaystyle \frac{4m^2-2mn}{2m^{3}n}}$;

${\displaystyle \frac{{2m-n}^{\mathrm{\setminus }9mn}}{m^{2}n}=}$${\displaystyle \frac{(2m-n)\cdot 9mn}{m^{2}n\cdot 9mn}=}$${\displaystyle \frac{18m^{2}n-9m{n}^2}{9m^3{n}^2}}$;

${\displaystyle \frac{{2m-n}^{\mathrm{\setminus }-7m^3{n}^2}}{m^{2}n}=}$${\displaystyle \frac{(2m-n)\cdot \left(-7m^3{n}^2\right)}{m^{2}n\cdot \left(-7m^3{n}^2\right)}=}$${\displaystyle \frac{-14m^4{n}^2+7m^3{n}^3}{-7m^5{n}^3}}$.