4. Сократите дроби: 1) (3x+3)/(x+1); 2) (2x−8)/(x−4); 3) (x+7)/(49−x²); 4) (−5−x)/((x+5)(x−5)); 5) (y−3)/((y−3)(y+3)); 6) (y²−6y+9)/(y−3); 7) (y+2)/(y²−4); 8) (3−y)/(y²−9); 9) (2−x+x+y)/(4−y²); 10) (y²+36−12y)/(6−y)².

Question

Вопрос:

Фото задания: 4. Сократите дроби: 1) (3x+3)/(x+1); 2) (2x−8)/(x−4); 3) (x+7)/(49−x²); 4) (−5−x)/((x+5)(x−5)); 5) (y−3)/((y−3)(y+3)); 6)…

4. Сократите дроби: 1) (3x+3)/(x+1); 2) (2x−8)/(x−4); 3) (x+7)/(49−x²); 4) (−5−x)/((x+5)(x−5)); 5) (y−3)/((y−3)(y+3)); 6) (y²−6y+9)/(y−3); 7) (y+2)/(y²−4); 8) (3−y)/(y²−9); 9) (2−x+x+y)/(4−y²); 10) (y²+36−12y)/(6−y)².

Accepted Answer

\(\dfrac{3x+3}{x+1}=\dfrac{3(x+1)}{x+1}=3\), \(x\ne-1\).
\(\dfrac{2x-8}{x-4}=\dfrac{2(x-4)}{x-4}=2\), \(x\ne4\).
\(\dfrac{x+7}{49-x^2}=\dfrac{x+7}{(7-x)(7+x)}=\dfrac{1}{7-x}\), \(x\ne-7,7\).
\(\dfrac{-5-x}{(x+5)(x-5)}=\dfrac{-(x+5)}{(x+5)(x-5)}=-\dfrac{1}{x-5}\), \(x\ne-5,5\).
\(\dfrac{y-3}{(y-3)(y+3)}=\dfrac{1}{y+3}\), \(y\ne-3,3\).
\(\dfrac{y^2-6y+9}{y-3}=\dfrac{(y-3)^2}{y-3}=y-3\), \(y\ne3\).
\(\dfrac{y+2}{y^2-4}=\dfrac{y+2}{(y-2)(y+2)}=\dfrac{1}{y-2}\), \(y\ne-2,2\).
\(\dfrac{3-y}{y^2-9}=\dfrac{-(y-3)}{(y-3)(y+3)}=-\dfrac{1}{y+3}\), \(y\ne-3,3\).
\(\dfrac{2-x+x+y}{4-y^2}=\dfrac{y+2}{(2-y)(2+y)}=\dfrac{1}{2-y}\), \(y\ne-2,2\).
\(\dfrac{y^2-12y+36}{(6-y)^2}=\dfrac{(y-6)^2}{(y-6)^2}=1\), \(y\ne6\).

Ответ: 1) 3; 2) 2; 3) \(\dfrac{1}{7-x}\); 4) \(-\dfrac{1}{x-5}\); 5) \(\dfrac{1}{y+3}\); 6) \(y-3\); 7) \(\dfrac{1}{y-2}\); 8) \(-\dfrac{1}{y+3}\); 9) \(\dfrac{1}{2-y}\); 10) 1.