6. 1) \(\frac{a}{ab-b^2}+\frac{2a}{b-a}\); 3) \(\frac{5b}{ax-ay}-\frac{3a}{by-bx}\)

1) Разложим знаменатели: \(ab-b^2=b(a-b)\), \(b-a=-(a-b)\).

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

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

3) \(ax-ay=a(x-y)\), а \(by-bx=-b(x-y)\).

\[\frac{5b}{a(x-y)}-\frac{3a}{-b(x-y)}=\frac{5b}{a(x-y)}+\frac{3a}{b(x-y)}.\]

Общий знаменатель: \(ab(x-y)\).

\[\frac{5b^2+3a^2}{ab(x-y)}.\]

Ответ: 1) \(\frac{a(1-2b)}{b(a-b)}\); 3) \(\frac{3a^2+5b^2}{ab(x-y)}\).