37. Сократите дробь: 1) (a − b)/(2(b − a)); 2) (3x − 6y)/(4y − 2x); 3) (m² − 5mn)/(15n − 3m); 4) (7a⁴ − a³b)/(b⁴ − 7ab³); 5) (x² − 25)/(5x² − x³); 6) (y² − 12y + 36)/(36 − y²).

1. \(\dfrac{a-b}{2(b-a)}=\dfrac{a-b}{-2(a-b)}=-\dfrac12\).
2. \(\dfrac{3x-6y}{4y-2x}=\dfrac{3(x-2y)}{-2(x-2y)}=-\dfrac32\).
3. \(\dfrac{m^2-5mn}{15n-3m}=\dfrac{m(m-5n)}{-3(m-5n)}=-\dfrac m3\).
4. \(\dfrac{7a^4-a^3b}{b^4-7ab^3}=\dfrac{a^3(7a-b)}{b^3(b-7a)}=-\dfrac{a^3}{b^3}\).
5. \(\dfrac{x^2-25}{5x^2-x^3}=\dfrac{(x-5)(x+5)}{x^2(5-x)}=-\dfrac{x+5}{x^2}\).
6. \(\dfrac{y^2-12y+36}{36-y^2}=\dfrac{(y-6)^2}{(6-y)(6+y)}=-\dfrac{y-6}{y+6}=\dfrac{6-y}{y+6}\).

Ответ: 1) \(-\dfrac12\); 2) \(-\dfrac32\); 3) \(-\dfrac m3\); 4) \(-\dfrac{a^3}{b^3}\); 5) \(-\dfrac{x+5}{x^2}\); 6) \(\dfrac{6-y}{y+6}\).