303 Вправа 303Алгебра 8 клас Бевз 2025 · § 7 · стор. 64

303. Спрости вираз.

а) ${\displaystyle \frac{a^3-1}{a-1}:(a^2+a+1)=}$${\displaystyle \frac{a^3-1}{a-1}\cdot \frac{1}{a^2+a+1}}$=

=${\displaystyle \frac{a^3-1}{(a-1)\cdot (a^2+a+1)}=}$${\displaystyle \frac{\cancel{\left(a^2+a+1\right)}\cancel{\left(a-1\right)}}{\cancel{\left(a^2+a+1\right)}\cancel{\left(a-1\right)}}=}$${\displaystyle 1}$;

б) ${\displaystyle \frac{1+x^3}{1+x}:(1-x+x^2)=}$${\displaystyle \frac{1+x^3}{1+x}\cdot \frac{1}{1-x+x^2}}$=

=${\displaystyle \frac{1+x^3}{(1+x)\cdot (1-x+x^2)}=}$${\displaystyle \frac{\cancel{\left(x+1\right)}\cancel{\left(x^2-x+1\right)}}{\cancel{\left(x+1\right)}\cancel{\left(x^2-x+1\right)}}=}$${\displaystyle 1}$.