67 Вправа 67Алгебра 8 клас Бевз 2025 · § 2 · стор. 20

67. Запиши вираз у вигляді дробу і скороти його.

а) ${\displaystyle 8a^2{c}^3:4a^3{c}^2=}$${\displaystyle \frac{2c\cdot \cancel{4a^2{c}^2}}{\cancel{4a^2{c}^2}\cdot a}=}$${\displaystyle \frac{2c}{a}}$;

б) ${\displaystyle 5a^3{x}^5:\left(25a^2{x}^4\right)=}$${\displaystyle \frac{ax\cdot \cancel{5a^2{x}^4}}{\cancel{5a^2{x}^4}\cdot 5}=}$${\displaystyle \frac{ax}{5}}$;

в) ${\displaystyle (n{x}^2+m{x}^2):(m+n)=}$${\displaystyle \frac{x^2\cancel{\left(n+m\right)}}{\cancel{\left(m+n\right)}}=}$${\displaystyle x^2}$;

г) ${\displaystyle (a^2-36):(36-a^2)=}$${\displaystyle \frac{\cancel{\left(a^2-36\right)}}{-\cancel{\left(a^2-36\right)}}=}$${\displaystyle -1}$;

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

д) ${\displaystyle (n{x}^3+n^4):(nx+n^2)=}$${\displaystyle \frac{n(x^3+n^3)}{n(x+n)}}$=

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