Упростите выражения: а) \(\frac{3a+12b}{6ab}\); б) \(\frac{15b-20c}{10b}\); в) \(\frac{2a-4}{3(a-2)}\); г) \(\frac{5x(y+2)}{6y+12}\); д) \(\frac{a-3b}{a^2-3ab}\); е) \(\frac{3x^2+15xy}{x+5y}\).

1. \(\frac{3a+12b}{6ab}=\frac{3(a+4b)}{6ab}=\frac{a+4b}{2ab}\).

2. \(\frac{15b-20c}{10b}=\frac{5(3b-4c)}{10b}=\frac{3b-4c}{2b}\).

3. \(\frac{2a-4}{3(a-2)}=\frac{2(a-2)}{3(a-2)}=\frac{2}{3}\), при \(a\ne2\).

4. \(\frac{5x(y+2)}{6y+12}=\frac{5x(y+2)}{6(y+2)}=\frac{5x}{6}\), при \(y\ne-2\).

5. \(\frac{a-3b}{a^2-3ab}=\frac{a-3b}{a(a-3b)}=\frac{1}{a}\), при \(a\ne0\) и \(a\ne3b\).

6. \(\frac{3x^2+15xy}{x+5y}=\frac{3x(x+5y)}{x+5y}=3x\), при \(x+5y\ne0\).

Ответ: а) \(\frac{a+4b}{2ab}\); б) \(\frac{3b-4c}{2b}\); в) \(\frac{2}{3}\); г) \(\frac{5x}{6}\); д) \(\frac{1}{a}\); е) \(3x\).