239 Вправа 239Алгебра 8 клас Бевз 2025 · § 5 · стор. 52

239. Find the product of fractions.

a) ${\displaystyle \frac{a^3+x^3}{a-x}\cdot \frac{a^2-2ax+x^2}{a^2-ax+x^2}=}$${\displaystyle \frac{(a^3+x^3)\cdot (a^2-2ax+x^2)}{(a-x)\cdot (a^2-ax+x^2)}}$=

=${\displaystyle \frac{(a+x)\cancel{\left(a^2-ax+x^2\right)}\cancel{\left(a-x\right)}(a-x)}{\cancel{\left(a^2-ax+x^2\right)}\cancel{\left(a-x\right)}}=}$${\displaystyle a^2-x^2}$;

b) ${\displaystyle \frac{a^6-1}{a^2+1}\cdot \frac{1+a^2}{a^4+1+a^2}=}$${\displaystyle \frac{(a^6-1)\cdot (1+a^2)}{(a^2+1)\cdot (a^4+1+a^2)}}$=

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