107 Вправа 107Алгебра 8 клас Тарасенкова 2025 · § 2 · стор. 32

107. Скоротіть дріб.

1) ${\displaystyle \frac{{(x+y)}^2-4xy}{x^2-xy}=}$${\displaystyle \frac{x^2+2xy+y^2-4xy}{x(x-y)}=}$${\displaystyle \frac{x^2-2xy+y^2}{x(x-y)}=}$${\displaystyle \frac{(x-y)\cancel{\left(x-y\right)}}{x\cancel{\left(x-y\right)}}=}$${\displaystyle \frac{x-y}{x}}$;

2) ${\displaystyle \frac{a^2-ab+3b-9}{a^2-2ab+b^2+3a-3b}=}$${\displaystyle \frac{(a^2-9)-(ab-3b)}{{(a-b)}^2+3(a-b)}=}$${\displaystyle \frac{(a-3)(a+3)-b(a-3)}{(a-b)(a-b+3)}=}$${\displaystyle \frac{(a-3)\cancel{\left(a+3-b\right)}}{(a-b)\cancel{\left(a-b+3\right)}}=}$${\displaystyle \frac{a-3}{a-b}}$.