180 Вправа 180Алгебра 8 клас Бевз 2025 · § 4 · стор. 39

180. Спрости вираз.

а) ${\displaystyle \frac{a^2}{{(a-3)}^2}-\frac{9}{{(a-3)}^2}=}$${\displaystyle \frac{a^2-9}{{(a-3)}^2}=}$${\displaystyle \frac{(a+3)\cancel{\left(a-3\right)}}{(a-3)\cancel{\left(a-3\right)}}=}$${\displaystyle \frac{a+3}{a-3}}$;

б) ${\displaystyle \frac{a^2}{{(a-b)}^3}-\frac{2ab-b^2}{{(a-b)}^3}=}$${\displaystyle \frac{a^2-(2ab-b^2)}{{(a-b)}^3}=}$${\displaystyle \frac{a^2-2ab+b^2}{{(a-b)}^3}}$=

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