302 Вправа 302Алгебра 8 клас Бевз 2025 · § 7 · стор. 64

302. Спрости вираз.

а) ${\displaystyle (n+\frac{1}{n})(n-\frac{1}{n}):(n^2-\frac{1}{n^2})}$;

1) ${\displaystyle (n+\frac{1}{n})(n-\frac{1}{n})=}$${\displaystyle n^2-{\left(\frac{1}{n}\right)}^2=}$${\displaystyle n^2-\frac{1}{n^2}}$;

2) ${\displaystyle (n^2-\frac{1}{n^2}):(n^2-\frac{1}{n^2})=}$${\displaystyle 1}$;

б) ${\displaystyle \frac{a}{c}\cdot \frac{a-c}{a+c}\cdot \frac{a+c}{a}=}$${\displaystyle \frac{\cancel{a}\cancel{\left(a+c\right)}(a-c)}{\cancel{a}c\cancel{\left(a+c\right)}}=}$${\displaystyle \frac{a-c}{c}}$.