【答案】
分析:(1)將原式中的三項(xiàng)化為最簡(jiǎn)二次根式,合并同類二次根式即可得到結(jié)果;
(2)利用多項(xiàng)式除以單項(xiàng)式的法則(用多項(xiàng)式的每一項(xiàng)除以單項(xiàng)式)變形,再利用二次根式的除法法則計(jì)算,即可得到結(jié)果;
(3)將方程左邊的多項(xiàng)式利用十字相乘法分解因式,然后利用兩數(shù)相乘積為0,兩因式中至少有一個(gè)為0轉(zhuǎn)化為兩個(gè)一元一次方程,求出一次方程的解即可得到原方程的解;
(4)將方程右邊的整體移項(xiàng)到左邊,兩項(xiàng)提取x-5分解因式,然后利用兩數(shù)相乘積為0,兩因式中至少有一個(gè)為0轉(zhuǎn)化為兩個(gè)一元一次方程,求出一次方程的解即可得到原方程的解.
解答:解:(1)原式=2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103201900855180080/SYS201311032019008551800015_DA/0.png)
+3
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103201900855180080/SYS201311032019008551800015_DA/1.png)
-4
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103201900855180080/SYS201311032019008551800015_DA/2.png)
=(2+3-4)
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103201900855180080/SYS201311032019008551800015_DA/3.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103201900855180080/SYS201311032019008551800015_DA/4.png)
;
(2)原式=2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103201900855180080/SYS201311032019008551800015_DA/5.png)
÷
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103201900855180080/SYS201311032019008551800015_DA/6.png)
-3
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103201900855180080/SYS201311032019008551800015_DA/7.png)
÷
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103201900855180080/SYS201311032019008551800015_DA/8.png)
=2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103201900855180080/SYS201311032019008551800015_DA/9.png)
-3
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103201900855180080/SYS201311032019008551800015_DA/10.png)
=2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103201900855180080/SYS201311032019008551800015_DA/11.png)
-3
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103201900855180080/SYS201311032019008551800015_DA/12.png)
=8-9=-1;
(3)x
2+2x-3=0,
因式分解得:(x-1)(x+3)=0,
可得出x-1=0或x+3=0,
解得:x
1=1,x
2=-3;
(4)3(x-5)
2=2(x-5),
移項(xiàng)得:3(x-5)
2-2(x-5)=0,
分解因式得:(x-5)[3(x-5)-2]=0,即(x-5)(3x-17)=0,
可得:x-5=0或3x-17=0,
解得:x
1=5,x
2=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103201900855180080/SYS201311032019008551800015_DA/13.png)
.
點(diǎn)評(píng):此題考查了解一元二次方程-因式分解法,以及二次根式的混合運(yùn)算,利用因式分解法解方程時(shí),首先將方程右邊化為0,左邊化為積的形式,然后利用兩數(shù)相乘積為0,兩因式中至少有一個(gè)為0轉(zhuǎn)化為兩個(gè)一元一次方程來求解.