Карточка 5: 1) 20m/(35m³) =; 2) 16x⁴y³/(24x²y⁵) =; 3) (100−n²)/(10−n) =; 4) (12z+36)/(6z+18) =; 5) (y²−y)/(y²−1) =; 6) (5v+10)/(v²+2v) =.

1. \(\dfrac{20m}{35m^3}=\dfrac{4}{7m^2}\).
2. \(\dfrac{16x^4y^3}{24x^2y^5}=\dfrac{2x^2}{3y^2}\).
3. \(\dfrac{100-n^2}{10-n}=\dfrac{(10-n)(10+n)}{10-n}=10+n\).
4. \(\dfrac{12z+36}{6z+18}=\dfrac{12(z+3)}{6(z+3)}=2\).
5. \(\dfrac{y^2-y}{y^2-1}=\dfrac{y(y-1)}{(y-1)(y+1)}=\dfrac{y}{y+1}\).
6. \(\dfrac{5v+10}{v^2+2v}=\dfrac{5(v+2)}{v(v+2)}=\dfrac5v\).

Ответ: 1) \(\frac4{7m^2}\); 2) \(\frac{2x^2}{3y^2}\); 3) \(10+n\); 4) \(2\); 5) \(\frac{y}{y+1}\); 6) \(\frac5v\).