240 Вправа 240Алгебра 8 клас Бевз 2025 · § 5 · стор. 52

240. Виконай множення дробів.

а) ${\displaystyle \frac{a}{5a-2}\cdot \frac{4-25a^2}{5a+2}=}$${\displaystyle \frac{a\cdot (4-25a^2)}{(5a-2)\cdot (5a+2)}}$=

=${\displaystyle -\frac{a\cancel{\left(5a+2\right)}\cancel{\left(5a-2\right)}}{\cancel{\left(5a+2\right)}\cancel{\left(5a-2\right)}}=}$${\displaystyle -a}$;

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

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