19. Сократите дробь: а) (a+b)/(a²−b²); б) (x−y)/(x²−y²); в) (a²−1)/(ab−b); г) (ab−3a)/(b²−9); д) (x²−y²)/(x²+2xy+y²); е) (a²−2ab+b²)/(a²−b²).

Question

Вопрос:

Фото задания

19. Сократите дробь: а) (a+b)/(a²−b²); б) (x−y)/(x²−y²); в) (a²−1)/(ab−b); г) (ab−3a)/(b²−9); д) (x²−y²)/(x²+2xy+y²); е) (a²−2ab+b²)/(a²−b²).

Accepted Answer

а) \(\dfrac{a+b}{a^2-b^2}=\dfrac{a+b}{(a-b)(a+b)}=\dfrac{1}{a-b}\).

б) \(\dfrac{x-y}{x^2-y^2}=\dfrac{x-y}{(x-y)(x+y)}=\dfrac{1}{x+y}\).

в) \(\dfrac{a^2-1}{ab-b}=\dfrac{(a-1)(a+1)}{b(a-1)}=\dfrac{a+1}{b}\).

г) \(\dfrac{ab-3a}{b^2-9}=\dfrac{a(b-3)}{(b-3)(b+3)}=\dfrac{a}{b+3}\).

д) \(\dfrac{x^2-y^2}{x^2+2xy+y^2}=\dfrac{(x-y)(x+y)}{(x+y)^2}=\dfrac{x-y}{x+y}\).

е) \(\dfrac{a^2-2ab+b^2}{a^2-b^2}=\dfrac{(a-b)^2}{(a-b)(a+b)}=\dfrac{a-b}{a+b}\).

Ответ: а) \(\dfrac{1}{a-b}\); б) \(\dfrac{1}{x+y}\); в) \(\dfrac{a+1}{b}\); г) \(\dfrac{a}{b+3}\); д) \(\dfrac{x-y}{x+y}\); е) \(\dfrac{a-b}{a+b}\).