№1. Сократите дроби: а) \(\frac{12x-3}{24x^2-6x}\); б) \(\frac{y+5}{y^2+10y+25}\); в) \(\frac{a^2-4a+4}{a^2-4}\); г) \(\frac{n^2-n+1}{n^3-n^2+n}\).

а) \(12x-3=3(4x-1)\), \(24x^2-6x=6x(4x-1)\).

\[\frac{12x-3}{24x^2-6x}=\frac{3(4x-1)}{6x(4x-1)}=\frac{1}{2x}.\]

б) \(y^2+10y+25=(y+5)^2\).

\[\frac{y+5}{y^2+10y+25}=\frac{y+5}{(y+5)^2}=\frac{1}{y+5}.\]

в) \(a^2-4a+4=(a-2)^2\), \(a^2-4=(a-2)(a+2)\).

\[\frac{a^2-4a+4}{a^2-4}=\frac{(a-2)^2}{(a-2)(a+2)}=\frac{a-2}{a+2}.\]

г) \(n^3-n^2+n=n(n^2-n+1)\).

\[\frac{n^2-n+1}{n^3-n^2+n}=\frac{n^2-n+1}{n(n^2-n+1)}=\frac{1}{n}.\]

Ответ: а) \(\frac{1}{2x}\); б) \(\frac{1}{y+5}\); в) \(\frac{a-2}{a+2}\); г) \(\frac{1}{n}\).