97° Вправа 97Алгебра 8 клас Тарасенкова 2025 · § 2 · стор. 31

97. Скоротіть дріб.

Пам’ятаємо: ${\displaystyle b-a=}$${\displaystyle -(a-b)}$.

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

2) ${\displaystyle \frac{4x+4y}{a(x+y)}=}$${\displaystyle \frac{4\cancel{\left(x+y\right)}}{a\cancel{\left(x+y\right)}}=}$${\displaystyle \frac{4}{a}}$;

3) ${\displaystyle \frac{3x-6y}{2x-4y}=}$${\displaystyle \frac{3\cancel{\left(x-2y\right)}}{2\cancel{\left(x-2y\right)}}=}$${\displaystyle \frac{3}{2}=}$${\displaystyle 1,5}$;

4) ${\displaystyle \frac{5a-5b}{b-a}=}$${\displaystyle \frac{5(a-b)}{-(a-b)}=}$${\displaystyle \frac{5\cancel{\left(a-b\right)}}{-\cancel{\left(a-b\right)}}=}$${\displaystyle -5}$;

5) ${\displaystyle \frac{3a-9c}{3c-a}=}$${\displaystyle \frac{3(a-3c)}{-(a-3c)}=}$${\displaystyle \frac{3\cancel{\left(a-3c\right)}}{-\cancel{\left(a-3c\right)}}=}$${\displaystyle -3}$;

6) ${\displaystyle \frac{4x-12y}{3ay-ax}=}$${\displaystyle \frac{4(x-3y)}{a(3y-x)}=}$${\displaystyle \frac{4\cancel{\left(x-3y\right)}}{-a\cancel{\left(x-3y\right)}}=}$${\displaystyle -\frac{4}{a}}$;

7) ${\displaystyle \frac{a^2-ab}{b^2-ab}=}$${\displaystyle \frac{a(a-b)}{b(b-a)}=}$${\displaystyle \frac{a\cancel{\left(a-b\right)}}{-b\cancel{\left(a-b\right)}}=}$${\displaystyle -\frac{a}{b}}$;

8) ${\displaystyle \frac{2ax-2ay}{3by-3bx}=}$${\displaystyle \frac{2a(x-y)}{3b(y-x)}=}$${\displaystyle \frac{2a\cancel{\left(x-y\right)}}{-3b\cancel{\left(x-y\right)}}=}$${\displaystyle -\frac{2a}{3b}}$.