$\frac{23}{126}$ и $\frac{47}{330}$
$ \begin{array}{r|l} 126 & 2\\ 63 & 3\\ 21 & 3\\ 7 & 7\\ 1 & \end{array} $
$126 = 2 * 3^2 * 7$

$ \begin{array}{r|l} 330 & 2\\ 165 & 3\\ 55 & 5\\ 11 & 11\\ 1 & \end{array} $
$330 = 2 * 3 * 5 * 11$
$НОК = 2 * 3^2 * 5 * 7 * 11 = 6930$
6930 : 126 = 55
$\frac{23}{126} = \frac{23 * 55}{126 * 55} = \frac{1265}{6930}$
6930 : 330 = 21
$\frac{47}{330} = \frac{47 * 21}{330 * 21} = \frac{987}{6930}$
$\frac{1265}{6930} > \frac{987}{6930}$, значит:
$\frac{23}{126} > \frac{47}{330}$

$\frac{59}{396}$ и $\frac{121}{840}$
$ \begin{array}{r|l} 396 & 2\\ 198 & 2\\ 99 & 3\\ 33 & 3\\ 11 & 11\\ 1 & \end{array} $
$396 = 2^2 * 3^2 * 11$

$ \begin{array}{r|l} 840 & 2\\ 420 & 2\\ 210 & 2\\ 105 & 3\\ 35 & 5\\ 7 & 7\\ 1 & \end{array} $
$840 = 2^3 * 3 * 5 * 7$
$НОК = 2^3 * 3^2 * 5 * 7 * 11 = 27720$
27720 : 396 = 70
$\frac{59}{396} = \frac{59 * 70}{396 * 70} = \frac{4130}{27720}$
27720 : 840 = 33
$\frac{121}{840} = \frac{121 * 33}{840 * 33} = \frac{3993}{27720}$
$\frac{4130}{27720} > \frac{3993}{27720}$, значит:
$\frac{59}{396} > \frac{121}{840}$