82 Вправа 82Алгебра 8 клас Бевз 2025 · § 2 · стор. 21

82. Скороти дріб.

а) ${\displaystyle \frac{25a{x}^2}{75a^{8}x}=}$${\displaystyle \frac{x\cdot \cancel{25ax}}{\cancel{25ax}\cdot 3a^7}=}$${\displaystyle \frac{x}{3a^7}}$;

б) ${\displaystyle \frac{125cm}{50c^{2}m}=}$${\displaystyle \frac{5\cdot \cancel{25cm}}{\cancel{25cm}\cdot 2c}=}$${\displaystyle \frac{5}{2c}}$;

в) ${\displaystyle \frac{3x^{2}c-6x{c}^2}{x^{2}c-2x{c}^2}=}$${\displaystyle \frac{3\cancel{xc}\cancel{\left(x-2c\right)}}{\cancel{xc}\cancel{\left(x-2c\right)}}=}$${\displaystyle 3}$;

г) ${\displaystyle \frac{a^2-n^2}{a^2-2an+n^2}=}$${\displaystyle \frac{\cancel{\left(a-n\right)}(a+n)}{(a-n)\cancel{\left(a-n\right)}}=}$${\displaystyle \frac{a+n}{a-n}}$;

ґ) ${\displaystyle \frac{ax+ay-az}{cx+cy-cz}=}$${\displaystyle \frac{a\cancel{\left(x+y-z\right)}}{c\cancel{\left(x+y-z\right)}}=}$${\displaystyle \frac{a}{c}}$;

д) ${\displaystyle \frac{a^3-1}{a^2+a+1}=}$${\displaystyle \frac{(a-1)\cancel{\left(a^2+a+1\right)}}{\cancel{a^2+a+1}}=}$${\displaystyle a-1}$.