45. Сократите дроби: 1) (2m² − 72n²)/(4m + 24n)²; 2) (a³ − 8)/(ab − a − 2b + 2); 3) (a³ + 2a²b + ab²)/(a³ − ab²).

1) \(\dfrac{2(m^2-36n^2)}{16(m+6n)^2}=\dfrac{2(m-6n)(m+6n)}{16(m+6n)^2}=\dfrac{m-6n}{8(m+6n)}\).

2) \(\dfrac{a^3-8}{ab-a-2b+2}=\dfrac{(a-2)(a^2+2a+4)}{(a-2)(b-1)}=\dfrac{a^2+2a+4}{b-1}\).

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

Ответ: 1) \(\dfrac{m-6n}{8(m+6n)}\); 2) \(\dfrac{a^2+2a+4}{b-1}\); 3) \(\dfrac{a+b}{a-b}\).