Карточка 6: 1) 24n/(32n⁵) =; 2) 27c²d⁴/(18c³d) =; 3) (4a²−9)/(2a+3) =; 4) (15w−45)/(10w−30) =; 5) (q²+4q)/(q²−16) =; 6) (6e−24)/(e²−4e) =.

1. \(\dfrac{24n}{32n^5}=\dfrac{3}{4n^4}\).
2. \(\dfrac{27c^2d^4}{18c^3d}=\dfrac{3d^3}{2c}\).
3. \(\dfrac{4a^2-9}{2a+3}=\dfrac{(2a-3)(2a+3)}{2a+3}=2a-3\).
4. \(\dfrac{15w-45}{10w-30}=\dfrac{15(w-3)}{10(w-3)}=\dfrac32\).
5. \(\dfrac{q^2+4q}{q^2-16}=\dfrac{q(q+4)}{(q-4)(q+4)}=\dfrac{q}{q-4}\).
6. \(\dfrac{6e-24}{e^2-4e}=\dfrac{6(e-4)}{e(e-4)}=\dfrac6e\).

Ответ: 1) \(\frac3{4n^4}\); 2) \(\frac{3d^3}{2c}\); 3) \(2a-3\); 4) \(\frac32\); 5) \(\frac{q}{q-4}\); 6) \(\frac6e\).