245 Вправа 245Алгебра 8 клас Бевз 2025 · § 5 · стор. 53

245. Перемнож дроби.

а) ${\displaystyle \frac{a+3}{10a^2}\cdot \frac{6-2a}{a}\cdot \frac{5a^3}{3-a}=}$${\displaystyle \frac{(a+3)\cdot (6-2a)\cdot 5a^3}{10a^2\cdot a\cdot (3-a)}}$=

=${\displaystyle \frac{\cancel{10}\cancel{a^3}(a+3)\cancel{\left(a-3\right)}}{\cancel{10}\cancel{a^3}\cancel{\left(a-3\right)}}=}$${\displaystyle a+3}$;

б) ${\displaystyle \frac{0,2}{x}\cdot \frac{x^2-1}{2x}\cdot \frac{5x}{x+1}=}$${\displaystyle \frac{0,2\cdot 5x\cdot (x^2-1)}{x\cdot 2x\cdot (x+1)}}$=

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

в) ${\displaystyle \frac{-6x^4}{35y^6{z}^3}\cdot \frac{5y^4{z}^7}{42x^6}\cdot \frac{-49x^3{y}^2}{z^4}=}$${\displaystyle \frac{-6x^4\cdot 5y^4{z}^7\cdot (-49x^3{y}^2)}{35y^6{z}^3\cdot 42x^6\cdot z^4}}$=

=${\displaystyle \frac{\cancel{6}\cancel{x^4}\cdot \cancel{5}\cancel{y^4}\cancel{z^7}\cdot \cancel{7}\cdot \cancel{7}x\cancel{x^2}\cancel{y^2}}{\cancel{5}\cdot \cancel{7}\cancel{y^6}\cancel{z^3}\cdot \cancel{6}\cdot \cancel{7}\cancel{x^6}\cdot \cancel{z^4}}=}$${\displaystyle x}$;

г) ${\displaystyle \frac{a^3{b}^2}{-20c^4}\cdot \frac{-5a^{4}c}{24b^5}\cdot \frac{16b^3{c}^3}{-30a^6}=}$${\displaystyle \frac{a^3{b}^2\cdot (-5a^{4}c)\cdot 16b^3{c}^3}{-20c^4\cdot 24b^5\cdot (-30a^6)}}$=

=${\displaystyle -\frac{\cancel{a^3}\cancel{b^2}\cdot \cancel{5}a\cancel{a^3}\cancel{c}\cdot \cancel{4}\cdot \cancel{4}\cancel{b^3}\cancel{c^3}}{\cancel{5}\cdot \cancel{4}\cancel{c^4}\cdot 6\cdot \cancel{4}\cancel{b^5}\cdot 30\cancel{a^6}}=}$${\displaystyle -\frac{a}{180}}$.