272 Вправа 272Алгебра 8 клас Бевз 2025 · § 6 · стор. 58

272. Знайди частку.

а) ${\displaystyle (a^2-4c^2):\frac{a-2c}{3ac}=}$${\displaystyle (a^2-4c^2)\cdot \frac{3ac}{a-2c}}$=

=${\displaystyle \frac{(a^2-4c^2)\cdot 3ac}{a-2c}=}$${\displaystyle \frac{3ac(a+2c)\cancel{\left(a-2c\right)}}{\cancel{\left(a-2c\right)}}=}$${\displaystyle 3ac\left(a+2c\right)}$;

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

=${\displaystyle \frac{x^2-y^2{z}^2}{(yz+x)\cdot (yz-x)}=}$${\displaystyle -\frac{\cancel{\left(x-yz\right)}\cancel{\left(yz+x\right)}}{\cancel{\left(x-yz\right)}\cancel{\left(yz+x\right)}}=}$${\displaystyle -1}$.