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).

а) Разложим знаменатель: \(a^2-b^2=(a-b)(a+b)\).

\[\frac{a+b}{a^2-b^2}=\frac{a+b}{(a-b)(a+b)}=\frac{1}{a-b}\]

б) \(x^2-y^2=(x-y)(x+y)\).

\[\frac{x-y}{x^2-y^2}=\frac{x-y}{(x-y)(x+y)}=\frac{1}{x+y}\]

в) \(a^2-1=(a-1)(a+1)\), \(ab-b=b(a-1)\).

\[\frac{a^2-1}{ab-b}=\frac{(a-1)(a+1)}{b(a-1)}=\frac{a+1}{b}\]

г) \(ab-3a=a(b-3)\), \(b^2-9=(b-3)(b+3)\).

\[\frac{ab-3a}{b^2-9}=\frac{a(b-3)}{(b-3)(b+3)}=\frac{a}{b+3}\]

д) \(x^2-y^2=(x-y)(x+y)\), \(x^2+2xy+y^2=(x+y)^2\).

\[\frac{x^2-y^2}{x^2+2xy+y^2}=\frac{(x-y)(x+y)}{(x+y)^2}=\frac{x-y}{x+y}\]

е) \(a^2-2ab+b^2=(a-b)^2\), \(a^2-b^2=(a-b)(a+b)\).

\[\frac{a^2-2ab+b^2}{a^2-b^2}=\frac{(a-b)^2}{(a-b)(a+b)}=\frac{a-b}{a+b}\]

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