Вариант 2. Сократите дроби: 1) 5a²/(6a); 2) c/(8c); 3) 5c⁴/(10c⁵); 4) x⁶y²/(x⁴y); 5) 42a⁴c³/(63a³c⁴); 6) a(x−2)/(b(x−2)); 7) 5y(b−7)/(10(b−7)²); 8) (3y+9)/(y²−9); 9) (x²−9)/(3x²+x³); 10) (a²+10a+25)/(3a+15).

1. \(\dfrac{5a^2}{6a}=\dfrac{5a}{6}\).
2. \(\dfrac{c}{8c}=\dfrac18\).
3. \(\dfrac{5c^4}{10c^5}=\dfrac1{2c}\).
4. \(\dfrac{x^6y^2}{x^4y}=x^2y\).
5. \(\dfrac{42a^4c^3}{63a^3c^4}=\dfrac{2a}{3c}\).
6. \(\dfrac{a(x-2)}{b(x-2)}=\dfrac ab\).
7. \(\dfrac{5y(b-7)}{10(b-7)^2}=\dfrac{y}{2(b-7)}\).
8. \(\dfrac{3y+9}{y^2-9}=\dfrac{3(y+3)}{(y-3)(y+3)}=\dfrac3{y-3}\).
9. \(\dfrac{x^2-9}{3x^2+x^3}=\dfrac{(x-3)(x+3)}{x^2(x+3)}=\dfrac{x-3}{x^2}\).
10. \(\dfrac{a^2+10a+25}{3a+15}=\dfrac{(a+5)^2}{3(a+5)}=\dfrac{a+5}{3}\).

Ответ: 1) \(\dfrac{5a}{6}\); 2) \(\dfrac18\); 3) \(\dfrac1{2c}\); 4) \(x^2y\); 5) \(\dfrac{2a}{3c}\); 6) \(\dfrac ab\); 7) \(\dfrac{y}{2(b-7)}\); 8) \(\dfrac3{y-3}\); 9) \(\dfrac{x-3}{x^2}\); 10) \(\dfrac{a+5}{3}\).