解:??$(1) \frac 1{x(x+1)}= \frac 1x-\frac 1{x+1} $??
??$ (2) ①$??原式??$ =\frac 1x-\frac 1{x+1}+\frac 1{x+1}- \frac 1{x+2}+···+\frac 1{x+2022}-\frac 1{x+2023}$??
??$ =\frac 1x-\frac 1{x+2023}$??
??$ = \frac {2023}{x(x+2023)} $??
②原式??$ =\frac 13 ×(\frac 1x-\frac 1{x+3}+\frac 1{x+3}-\frac 1{x+6}+···+\frac 1{x+27}-\frac 1{x+30})$??
??$ =\frac 13 ×(\frac 1x-\frac 1{x+30})$??
??$ = \frac {10}{x(x+30)} $??