300 Вправа 300Алгебра 8 клас Бевз 2025 · § 7 · стор. 64

300. Спрости вираз.

а) ${\displaystyle (a+\frac{x}{c}):(a+\frac{x}{c})}$;

1) ${\displaystyle \frac{a^{\mathrm{\setminus }c}}{1}+\frac{x}{c}=}$${\displaystyle \frac{ac+x}{c}}$;

2) ${\displaystyle \frac{ac+x}{c}:\frac{ac+x}{c}=}$${\displaystyle \frac{ac+x}{c}\cdot \frac{c}{ac+x}=}$${\displaystyle \frac{\cancel{c}\cancel{\left(ac+x\right)}}{\cancel{c}\cancel{\left(ac+x\right)}}=}$${\displaystyle 1}$;

б) ${\displaystyle (1+\frac{a}{n}):\frac{n+a}{n}}$;

1) ${\displaystyle \frac{1^{\mathrm{\setminus }n}}{1}+\frac{a}{n}=}$${\displaystyle \frac{n+a}{n}}$;

2) ${\displaystyle \frac{a+n}{n}:\frac{n+a}{n}=}$${\displaystyle \frac{a+n}{n}\cdot \frac{n}{n+a}=}$${\displaystyle \frac{\cancel{n}\cancel{\left(a+n\right)}}{\cancel{n}\cancel{\left(a+n\right)}}=}$${\displaystyle 1}$.