【答案】
分析:(1)根据零指数幂、特殊角的三角函数值、绝对值性质、二次根式化简分别进行分析,然后根据实数的运算法则求得计算结果;
(2)根据分式化简法则首先通分,然后去括号,化简代入值求出;
(3)根据解不等式的方法,分别解一元一次不等式即可得出公共解集.
解答:解:(1)|1-
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/0.png)
|-sin60°+(π-3.14)
-
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/1.png)
,
=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/2.png)
-1-
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/3.png)
+1-
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/4.png)
,
=0;
(2)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/5.png)
,
=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/6.png)
÷
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/7.png)
,
=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/8.png)
×
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/9.png)
,
=x-1,(注意x不能取1,-1,0)
当x=2时,代入原式得:
原式=x-1=2-1=1;
(3)组
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/10.png)
,
由x-
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/11.png)
(2x-1)≤4,
解得:
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/12.png)
,
由
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/13.png)
>2x-1,
解得:x<3,
∴
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022160028458836748/SYS201310221600284588367016_DA/14.png)
∵x是整数,
∴x=-1,0,1,2,
点评:此题主要考查了实数的运算以及不等式组的解法和分式方程的化简求值,在运算过程中注意运算的顺序以及运算方法,正确的运算方法可以降低计算量.