Вариант 4: 1) (15ac⁸)/(18a⁵c²); 2) (36−6x)/(36−x²); 3) (x²+8x+16)/(4x+16); 4) (y⁶+y⁴)/(y⁶+y⁹); 5) (8y−12y²)/(3y−2); 6) (a²−25)/(25−10a+a²); 7) (x³+27)/(x³+3x²−2x−6).

Question

Вопрос:

Фото задания: Вариант 4: 1) (15ac⁸)/(18a⁵c²); 2) (36−6x)/(36−x²); 3) (x²+8x+16)/(4x+16); 4) (y⁶+y⁴)/(y⁶+y⁹); 5) (8y−12y²)/(3y−2); 6)…

Вариант 4: 1) (15ac⁸)/(18a⁵c²); 2) (36−6x)/(36−x²); 3) (x²+8x+16)/(4x+16); 4) (y⁶+y⁴)/(y⁶+y⁹); 5) (8y−12y²)/(3y−2); 6) (a²−25)/(25−10a+a²); 7) (x³+27)/(x³+3x²−2x−6).

Accepted Answer

\(\frac{15ac^8}{18a^5c^2}=\frac{5c^6}{6a^4}\).
\(\frac{36-6x}{36-x^2}=\frac{6(6-x)}{(6-x)(6+x)}=\frac6{x+6}\).
\(\frac{x^2+8x+16}{4x+16}=\frac{(x+4)^2}{4(x+4)}=\frac{x+4}{4}\).
\(\frac{y^6+y^4}{y^6+y^9}=\frac{y^4(y^2+1)}{y^6(y^3+1)}=\frac{y^2+1}{y^2(y^3+1)}\).
\(\frac{8y-12y^2}{3y-2}=\frac{4y(2-3y)}{3y-2}=-4y\).
\(\frac{a^2-25}{25-10a+a^2}=\frac{(a-5)(a+5)}{(a-5)^2}=\frac{a+5}{a-5}\).
\(\frac{x^3+27}{x^3+3x^2-2x-6}=\frac{(x+3)(x^2-3x+9)}{(x+3)(x^2-2)}=\frac{x^2-3x+9}{x^2-2}\).

Ответ: 1) \(\frac{5c^6}{6a^4}\); 2) \(\frac6{x+6}\); 3) \(\frac{x+4}{4}\); 4) \(\frac{y^2+1}{y^2(y^3+1)}\); 5) \(-4y\); 6) \(\frac{a+5}{a-5}\); 7) \(\frac{x^2-3x+9}{x^2-2}\).