【答案】
分析:(1)首先對每項(xiàng)進(jìn)行化簡,進(jìn)行負(fù)整數(shù)指數(shù)冪和零指數(shù)冪的運(yùn)算,然后再進(jìn)行加減運(yùn)算即可,注意-1的奇次方仍為-1,非零數(shù)的零次方為1,(2)首先方程兩邊同乘以最簡公分母(x-1)(x+2),把分式方程轉(zhuǎn)化為整式方程進(jìn)行求解,然后把x的值代入到最簡公分母進(jìn)行檢驗(yàn).
解答:解:(1)原式=2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164346518892652/SYS201310221643465188926018_DA/0.png)
+2-1-1=2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164346518892652/SYS201310221643465188926018_DA/1.png)
,
(2)方程兩邊同乘以最簡公分母(x-1)(x+2)得:x(x+2)-(x+2)(x-1)=3(x-1),
整理得:-2x=-5,
∴x=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164346518892652/SYS201310221643465188926018_DA/2.png)
,
檢驗(yàn):當(dāng)x=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164346518892652/SYS201310221643465188926018_DA/3.png)
時(shí),(x-1)(x+2)=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164346518892652/SYS201310221643465188926018_DA/4.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164346518892652/SYS201310221643465188926018_DA/5.png)
≠0,
∴x=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022164346518892652/SYS201310221643465188926018_DA/6.png)
是原方程的解.
點(diǎn)評:本題主要考查解分式方程,零指數(shù)冪和負(fù)整數(shù)指數(shù)冪的運(yùn)算,絕對值的定義等知識點(diǎn),關(guān)鍵在于根據(jù)相關(guān)的運(yùn)算法則進(jìn)行計(jì)算,正確的把分式方程轉(zhuǎn)化為整式方程,注意,求出x的值后,要進(jìn)行檢驗(yàn).