1.(09湖南怀化)先化简,再求值:其中
[关键词]分式化简、无理数运算
[答案]解:
52.(2009年咸宁市)先将代数式化简,再从的范围内选取一个合适的整数代入求值.
34.(2)(2009年宜宾)先化简,再求值:,其中.
[关键词]分式运算
[答案]原式===.
当时,原式==3.
35(2009年重庆)先化简,再求值:,其中.
[关键词]分式运算
[答案]原式
.
当时,原式.
36先化简,再求值:·,其中a=+1(精确到001).
[关键词]分式化简求值
[答案]B
原式=
=
=2(a-1).
∵a=+1,
∴原式=2(a-1)
=2(+1-1)
=2≈529.
[关键词]分式化简
37(2009年莆田)先化简,再求值:其中.
[关键词]分式、化简求值
.解:原式=··········································································· 6分
=······································································································· 7分
当时原式=····················································································· 8分
注:(各2分)
38(2009年莆田)面对全球金融危机的挑战,我国政府毅然启动内需,改善民生.国务院决定从2009年2月1日起,“家电下乡”在全国范围内实施,农民购买人选产品,政府按原价购买总额的13%给予补贴返还.某村委会组织部分农民到商场购买人选的同一型号的冰箱、电视机两种家电,已知购买冰箱的数量是电视机的2倍,且按原价购买冰箱总额为40000元、电视机总额为15000元.根据“家电下乡”优惠政策,每台冰箱补贴返还的金额比每台电视机补贴返还的金额多65元,求冰箱、电视机各购买多少台?
(1)设购买电视机台,依题意填充下列表格:
项目 家电种类 |
购买数量(台) |
原价购买总额(元) |
政府补贴返还比例 |
补贴返还总金额(元) |
每台补贴返还金额(元) |
冰箱 |
|
40
000 |
13% |
|
|
电视机 |
|
15
000 |
13% |
|
|
(2)列出方程(组)并解答.
[关键词]分式方程、方程
(1)每个空格填对得1分,满分5分.
|
40 000 |
13% |
或5200 |
或或 |
|
15 000 |
13% |
15 000×13%或1950 |
或 |
(2)解:依题意得-·························································· 7分
解得························································································································· 8分
经检验是原分式方程的解·························································································· 9分
答:冰箱、电视机分别购买20台、10台 10分
39(2009年本溪)17.先化简,再求值:,其中.
[关键词]分式的计算
[答案]解:
当时,原式.
40(2009年本溪)19.“五·一”期间,九年一班同学从学校出发,去距学校6千米的本溪水洞游玩,同学们分为步行和骑自行车两组,在去水洞的全过程中,骑自行车的同学比步行的同学少用40分钟,已知骑自行车的速度是步行速度的3倍.
(1)求步行同学每分钟走多少千米?
(2)右图是两组同学前往水洞时的路程(千米)
与时间(分钟)的函数图象.
完成下列填空:
①表示骑车同学的函数图象是线段 ;
②已知点坐标,则点的坐标为( ).
[关键词]分式方程
[答案]
(1)解:设步行同学每分钟走千米,则骑自行车同学每分钟走千米.
根据题意,得:
经检验,是原方程的解答:步行同学每分钟走千米.(2)①②.
41(2009宁夏)18.解分式方程:.
[关键词]分式计算
[答案]解:去分母得:整理方程得:
经检验是原方程的解.
原方程的解为.
42(2009肇庆)20.已知,求代数式的值.
[关键词]分式计算
[答案]解:
∵,∴原式.
43(2009年南充)化简:.
[关键词]分式的化简
[答案]解:原式=
=
44(2009年哈尔滨)先化简.再求代数式的值. 其中a=tan60°-2sin30°.
[关键词]约分与通分,分式运算
[答案]此题考查了分式的混合运算,计算时,可以先算括号里面的,也可利用乘法分配律进行计算,注意约分.另外在计算a的值时,特殊的三角函数要记准确.
解:原式.
当a=tan60°-2sin30°时,原式.
45(2009年牡丹江)先化简:并任选一个你喜欢的数代入求值.
[关键词]约分与通分,分式运算
[答案]解:原式=
46(2009年凉山州)先化简,再选择一个你喜欢的数(要合适哦!)代入求值:
.
[关键词]分式的运算
[答案]
取时,原式.
47(2009年益阳市)先化简,再求值:,其中.
[关键词]分式化简求值
[答案]解:原式=
=
=
当时
原式=
=
48(2009年衡阳市)先化简,再求值:,其中.
[关键词]分式化简求值
[答案]解:原式
把代入得:
原式
49(2009年株洲市)先化简,再求值:,其中.
[关键词]分式运算
[答案]化简,得:原式=
当时,得:原式
50(2009年重庆市江津区)先化简,再求值
,其中 = 3 .
[关键词]分式运算
[答案]解:原式=
=
=
当时,原式=
51(2009年河北)已知a = 2,,求÷的值.
[关键词]分式化简求值
解:原式=
=.
当a = 2,时,
原式 = 2.
31.(2009年益阳市)先化简,再求值:,其中.
[关键词]分式化简求值
[答案]解:原式=
=
=
当时
原式=
=
32(2009年衡阳市)先化简,再求值:,其中.
[关键词]分式化简求值
[答案]解:原式
把代入得:
原式
33(2009年日照)化简:.
[关键词]分式混合运算
[答案]:原式=
=
=
=
=1.
25.原式=
=.
当x=时,原式=.
26(2009泰安)先化简、再求值:。
[关键词]分式求值
[答案]解:原式=………………………………2分
=………………………………………………3分
=………………………………………4分
=………………………………………………………5分
27(2009江西)当……………………
先化简,再求值:
其中
[关键词]分式求值
[答案]解:÷= 3分
=x+4············································································· 5分
当x =3时,原式=3+4
=7·································································································· 7分
28(2009年牡丹江市)先化简:并任选一个你喜欢的数代入求值.
[关键词]分式的化简求值
[答案]原式===.取0和1以外的任何数.
29(2009年湘西自治州)17.先化简再计算:,其中=3,=2
[关键词]分解因式,分式运算
[答案]解:原式=
=x+y-2x+y
=-x+2y
因为 x=3,y=2
所以原式=-3+4=1
30(2009年清远)化简:
[关键词]约分与通分,分式运算
[答案]解:原式=
=
19.(2009年上海市)计算:.
[关键词]分式的化简
[答案]解:原式=
=
=
=
11(2009重庆綦江)先化简,再求值:,其中.
[关键词]分式的运算
[答案]
原式=
=
=
当时,原式=.
12 (2009年安顺)先化简,再求值:,其中
[关键词]分式运算,实数运算
[答案]
13(2009年安顺)下表为抄录北京奥运会官方票务网公布的三种球类比赛的部分门票价格,某公司购买的门票种类、数量绘制的统计图表如下:
依据上列图表,回答下列问题:
(1) 其中观看足球比赛的门票有_____张;观看乒乓球比赛的门票占全部门票的_____%;
(2) 公司决定采用随机抽取的方式把门票分配给100名员工,在看不到门票的条件下,每人抽取一张(假设所有的门票形状、大小、质地完全相同且充分洗匀),问员工小华抽到男篮门票的概率是_____;
(3) 若购买乒乓球门票的总款数占全部门票总款数的,求每张乒乓球门票的价格。
[关键词]频率估计概率,直方图,分式方程
[答案](1)50,20
(2)
(3)依题意,有= .
解得x ≈530 . 经检验,x =530是原方程的解.
答:每张乒乓球门票的价格约为530元.
14(2009山西省太原市) 化简:
[关键词]分式运算
[答案]
解:原式=···················································· 2分
=···························································································································································· 4分
=1. 5分
15(2009襄樊市)计算:
[关键词]分式运算
[答案]
解:原式=····································································· 2分
=················································································ 3分
··············································································· 4分
········································································································· 5分
162009湖北省荆门市)已知x=2+,y=2,计算代数式的值.
[关键词]分式运算
[答案]
解:=
==························································································· 4分
当x=2+,y=2-时,=-4··································· 6分
17(2009年贵州省黔东南州)先化简,再求值:,其中.
[关键词]分式运算
[答案]解:原式=
=.
将代入得:原式=.
18(2009年江苏省).
[关键词]分式运算
[答案]原式.
19 (2009年浙江省绍兴市)化简:·.
[关键词]分式运算
[答案]原式=·=.
20(2009年齐齐哈尔市)先化简:,当时,请你为任选一个适当的数代入求值.
[关键词]分式运算、最简分式
[答案]原式=
=
=
21(2009桂林百色)20.(本题满分6分)先化简,再求值:,
其中.
[关键词]分式化简
[答案]20.解:原式································ 2分
······························································································ 3分
··········································································································· 4分
·················································································································· 5分
把 ··························································· 6分
22(2009恩施市)求代数式的值:,其中.
[关键词]分式的化简与求值
[答案]解:原式=
=
=
=
当时
上式
23(2009年娄底)先化简,再求值:
+÷,其中x=.
[关键词]分式、化简求值
[答案]解:原式=
=
=
=
=
当x=时,原式=
=1-
24(2009年广西南宁)先化简,再求值:
,其中
[关键词]分式
[答案]解:
=························································································· 3分
······················································································································· 4分
当时,原式···················································································· 5分
······························································································· 6分
25(2009年河南)先化简,然后从中选取一个你认为合适的数作为x的值代入求值.
[关键词]分式的化简求值
[答案]
5.(2009年长春)先化简,再求值:,其中
[关键词]约分与通分,分式运算
[答案]原式=
当x=2时,原式=
6(2009年锦州)先化简,再任选一个你喜欢的数代入求值.
[关键词]约分与通分,分式运算
[答案]
解:
= ……3分
= ……4分
= ……5分
=. ……6分
(x只要不取0,±2均可)
如当x=1时, ……7分
原式==0. ……8分
7(2009年郴州市)化简:
[关键词]化简
[答案]解:原式=
=
=1+1
=2
8(2009年常德市)化简:
[关键词]通分
[答案]原式=
=
=
9(2009年桂林市、百色市)(本题满分6分)先化简,再求值:,
其中.
[关键词]化简
[答案]解:原式
把
10(2009武汉)18.先化简,再求值:,其中.
[关键词]分式的化简求值
[答案]解:原式==
当时,原式.
4.(2009仙桃)先化简,再求值:,其中x=2-.
[关键词]分式化简.
[答案] 原式=
当时,原式
1(2009年株洲市)先化简,再求值:,其中.
[关键词]分式运算
[答案]化简,得:原式=
当时,得:原式
2.(2009年重庆市江津区)先化简,再求值
,其中 = 3 .
[关键词]分式运算
[答案]解:原式===
当时,原式=
3(2009年泸州)化简:
[关键词]分式化简.
[答案]
20.(2009临沂)化简的结果是( )
A. B. C. D.
[关键词]分式化简
[答案]A
21(2009年肇庆市)若分式的值为零,则的值是( )
A.3 B. C. D.0
[关键词]分式值为零
[答案]A
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