270 Вправа 270Алгебра 8 клас Бевз 2025 · § 6 · стор. 58

270. Знайди частку.

а) ${\displaystyle \frac{3a}{x-y}:\frac{6a^2}{{(x-y)}^2}=}$${\displaystyle \frac{3a}{x-y}\cdot \frac{{(x-y)}^2}{6a^2}=}$${\displaystyle \frac{3a\cdot {(x-y)}^2}{(x-y)\cdot 6a^2}}$=

=${\displaystyle \frac{\cancel{3}\cancel{a}\cancel{\left(x-y\right)}(x-y)}{2\cdot \cancel{3}\cancel{a}a\cancel{\left(x-y\right)}}=}$${\displaystyle \frac{x-y}{2a}}$;

б) ${\displaystyle \frac{x^2-2x+1}{3x^2}:\frac{{(x-1)}^2}{3x^3}=}$${\displaystyle \frac{x^2-2x+1}{3x^2}\cdot \frac{3x^3}{{(x-1)}^2}}$=

=${\displaystyle \frac{(x^2-2x+1)\cdot 3x^3}{3x^2\cdot {(x-1)}^2}=}$${\displaystyle \frac{\cancel{3}\cancel{x^2}x\cancel{{\left(x-1\right)}^2}}{\cancel{3}\cancel{x^2}\cancel{{\left(x-1\right)}^2}}=}$${\displaystyle x}$;

в) ${\displaystyle (a^2-b^2):\frac{a+b}{a-b}=}$${\displaystyle (a^2-b^2)\cdot \frac{a-b}{a+b}}$=

=${\displaystyle \frac{(a^2-b^2)\cdot (a-b)}{a+b}=}$${\displaystyle \frac{\cancel{\left(a+b\right)}{(a-b)}^2}{\cancel{\left(a+b\right)}}=}$${\displaystyle {\left(a-b\right)}^2}$.