61 Вправа 61Алгебра 8 клас Бевз 2025 · § 2 · стор. 19

61. Скороти дріб, розклавши, якщо потрібно, чисельник і знаменник дробу на множники.

а) ${\displaystyle \frac{a(b-x)}{xb-x^2}=}$${\displaystyle \frac{a\cancel{\left(b-x\right)}}{x\cancel{\left(b-x\right)}}=}$${\displaystyle \frac{a}{x}}$;

б) ${\displaystyle \frac{a(4a-3)}{4a^2-3a}=}$${\displaystyle \frac{\cancel{a}\cancel{\left(4a-3\right)}}{\cancel{a}\cancel{\left(4a-3\right)}}=}$${\displaystyle 1}$;

в) ${\displaystyle \frac{x^2(5x-1)}{5x{y}^2-y^2}=}$${\displaystyle \frac{x^2\cancel{\left(5x-1\right)}}{y^2\cancel{\left(5x-1\right)}}=}$${\displaystyle \frac{x^2}{y^2}}$;

г) ${\displaystyle \frac{xc-mc}{ax-am}=}$${\displaystyle \frac{c\cancel{\left(x-m\right)}}{a\cancel{\left(x-m\right)}}=}$${\displaystyle \frac{c}{a}}$;

ґ) ${\displaystyle \frac{a{x}^2-x^3}{ax-x^2}=}$${\displaystyle \frac{x\cancel{x}\cancel{\left(a-x\right)}}{\cancel{x}\cancel{\left(a-x\right)}}=}$${\displaystyle x}$;

д) ${\displaystyle \frac{2x-x^4}{2y-x^{3}y}=}$${\displaystyle \frac{x\cancel{\left(2-x^3\right)}}{y\cancel{\left(2-x^3\right)}}=}$${\displaystyle \frac{x}{y}}$.