Вариант 1: 1) (14x³y²)/(21xy⁶); 2) (x²−9)/(3x−9); 3) (2a+18)/(a²+18a+81); 4) (x⁷+x⁵)/(x⁷+x⁹); 5) (15y−10y²)/(2y−3); 6) (y²−8y+16)/(16−y²); 7) (x³−3x²−2x+6)/(x³−27).

Question

Вопрос:

Фото задания: Вариант 1: 1) (14x³y²)/(21xy⁶); 2) (x²−9)/(3x−9); 3) (2a+18)/(a²+18a+81); 4) (x⁷+x⁵)/(x⁷+x⁹); 5) (15y−10y²)/(2y−3); 6)…

Вариант 1: 1) (14x³y²)/(21xy⁶); 2) (x²−9)/(3x−9); 3) (2a+18)/(a²+18a+81); 4) (x⁷+x⁵)/(x⁷+x⁹); 5) (15y−10y²)/(2y−3); 6) (y²−8y+16)/(16−y²); 7) (x³−3x²−2x+6)/(x³−27).

Accepted Answer

\(\frac{14x^3y^2}{21xy^6}=\frac{2x^2}{3y^4}\).
\(\frac{x^2-9}{3x-9}=\frac{(x-3)(x+3)}{3(x-3)}=\frac{x+3}{3}\).
\(\frac{2a+18}{a^2+18a+81}=\frac{2(a+9)}{(a+9)^2}=\frac{2}{a+9}\).
\(\frac{x^7+x^5}{x^7+x^9}=\frac{x^5(x^2+1)}{x^7(x^2+1)}=\frac1{x^2}\).
\(\frac{15y-10y^2}{2y-3}=\frac{5y(3-2y)}{2y-3}=-5y\).
\(\frac{y^2-8y+16}{16-y^2}=\frac{(y-4)^2}{(4-y)(4+y)}=\frac{4-y}{4+y}\).
\(\frac{x^3-3x^2-2x+6}{x^3-27}=\frac{(x-3)(x^2-2)}{(x-3)(x^2+3x+9)}=\frac{x^2-2}{x^2+3x+9}\).

Ответ: 1) \(\frac{2x^2}{3y^4}\); 2) \(\frac{x+3}{3}\); 3) \(\frac2{a+9}\); 4) \(\frac1{x^2}\); 5) \(-5y\); 6) \(\frac{4-y}{4+y}\); 7) \(\frac{x^2-2}{x^2+3x+9}\).