Вариант 1. Сократите дроби: 1) 3x²/(7x); 2) a/(15a); 3) 8x³/(15x⁴); 4) a²b⁵/(ab⁷); 5) 30a²c³/(48a³c²); 6) x(a+3)/(y(a+3)); 7) 3a(b−2)/(6(b−2)²); 8) (5x−10)/(x²−4); 9) (y²−16)/(4y²−y³); 10) (x²−4x+4)/(3x−6).

1. \(\dfrac{3x^2}{7x}=\dfrac{3x}{7}\).
2. \(\dfrac{a}{15a}=\dfrac1{15}\).
3. \(\dfrac{8x^3}{15x^4}=\dfrac{8}{15x}\).
4. \(\dfrac{a^2b^5}{ab^7}=\dfrac{a}{b^2}\).
5. \(\dfrac{30a^2c^3}{48a^3c^2}=\dfrac{5c}{8a}\).
6. \(\dfrac{x(a+3)}{y(a+3)}=\dfrac{x}{y}\).
7. \(\dfrac{3a(b-2)}{6(b-2)^2}=\dfrac{a}{2(b-2)}\).
8. \(\dfrac{5x-10}{x^2-4}=\dfrac{5(x-2)}{(x-2)(x+2)}=\dfrac5{x+2}\).
9. \(\dfrac{y^2-16}{4y^2-y^3}=\dfrac{(y-4)(y+4)}{y^2(4-y)}=-\dfrac{y+4}{y^2}\).
10. \(\dfrac{x^2-4x+4}{3x-6}=\dfrac{(x-2)^2}{3(x-2)}=\dfrac{x-2}{3}\).

Ответ: 1) \(\dfrac{3x}{7}\); 2) \(\dfrac1{15}\); 3) \(\dfrac{8}{15x}\); 4) \(\dfrac{a}{b^2}\); 5) \(\dfrac{5c}{8a}\); 6) \(\dfrac{x}{y}\); 7) \(\dfrac{a}{2(b-2)}\); 8) \(\dfrac5{x+2}\); 9) \(-\dfrac{y+4}{y^2}\); 10) \(\dfrac{x-2}{3}\).