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電子課本網(wǎng) 第63頁

第63頁

信息發(fā)布者:
解: 原式?$ = \frac {x^2-y^2}{x-y}=x+y$?
將?$y=-x+8$?代入原式,
原式?$=x+(-x+8)=8$?
解:??$(1)A=\frac {(x-1)^2}{(x+1)(x-1)}-\frac x{x+1}=-\frac 1{x+1}$??
??$(2)$??不等式組解得:??$ -3≤x≤-1$??
∵??$x$??為整數(shù),且??$x^2-1≠0,$??即:??$x≠±1$??
∴??$x=-2$??
∴??$A=1$??
解:??$ \frac A{x-1}- \frac B{2-x}=\frac {A(2-x)-B(x-1)}{(x-1)(2-x)}=\frac {(-A-B) x+(B+2 \mathrm A)}{(x-1)(2-x)}= \frac {(A+B) x-(B+2 \mathrm A)}{(x-1)(x-2)} ,$??
由題意可得:??$\begin{cases}{A+B=2,}\\{-B-2A=-6,}\end{cases}$??解得:??$\begin{cases}{A=4,}\\{B=-2,}\end{cases}$??
∴??$A-B=4-(-2)=6 $??
解:??$(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)} $??