标题

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2019年中考第一轮中考复习数与式模块复习(分式专题讲义)_2018年中考分式真题汇编

一、2018年中考真题分式专题知识点分析

知识点(解答计算题)题量占比
分式的化简求值3774.00%
分式的加减法12.00%
分式的混合运算714.00%
实数的运算36.00%
绝对值12.00%
多项式乘多项式12.00%

二、 2018年中考真题分式专题难易度分析

试题难易度题量题号题量占比
122%
较易163,5,6,7,9,10,13,14,15,20,24,25,26,27,28,2932%
中档331,4,8,11,12,16,17,18,19,21,22,23,30,31,
32,33,34,35,36,37,38,39,40,41,42,43,44,
45,46,47,48,49,50
66%
较难000%
000%

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2018年全国各省市中考真题汇编—分式解答题计算

一.解答题(共50小题)

1.(2018•百色)已知\({a^2} = 19\),求\(\frac{2}{{a + 1}} – \frac{{2a}}{{{a^2} – 1}} – \frac{1}{{18}}\)的值.

2.(2018•牡丹江)先化简,再求值:\(\frac{{x}^{2}-1}{{x}^{2}-2x+1}· \frac{1}{x+1}-\frac{1}{x}\),其中\(x = 2\).

3.(2018•青海)先化简,再求值:\((1 – \frac{1}{{m – 1}}) \div \frac{{{m^2} – 4m + 4}}{{{m^2} – m}}\),其中\(m = 2 + \sqrt 2 \).

4.(2018•益阳)化简:\((x-y+\frac{{y}^{2}}{x+y})· \frac{x+y}{x}\).

5.(2018•巴中)先化简,再求值:\((\frac{1}{{{x^2} – 4}} + \frac{1}{{x + 2}}) \div \frac{{x – 1}}{{x – 2}}\),其中\(x =  – \frac{3}{2}\).

6.(2018•宁夏)先化简,再求值:\((\frac{1}{{x + 3}} – \frac{1}{{3 – x}}) \div \frac{2}{{x – 3}}\),其中,\(x = \sqrt 3  – 3\).

7.(2018•葫芦岛)先化简,再求值:\((\frac{{2a}}{{a – 1}} – \frac{{{a^2} – a}}{{{a^2} – 2a + 1}}) \div \frac{a}{{a + 1}}\),其中\(a = {3^{ – 1}} + 2\sin 30^\circ \).

8.(2018•莱芜)先化简,再求值:\((\frac{3}{{a – 1}} + \frac{{a – 3}}{{{a^2} – 1}}) \div \frac{a}{{a + 1}}\),其中\(a = \sqrt 2  + 1\).

9.(2018•昆明)先化简,再求值:\((\frac{1}{{a – 2}} + 1) \div \frac{{{a^2} – 1}}{{3a – 6}}\),其中\(a = \tan 60^\circ  – | – 1|\).

10.(2018•黑龙江)先化简,再求值:\((1 – \frac{a}{{{a^2} + a}}) \div \frac{{{a^2} – 1}}{{{a^2} + 2a + 1}}\),其中\(a = \sin 30^\circ \).

11.(2018•遂宁)先化简,再求值\(\frac{{x}^{2}-{y}^{2}}{{x}^{2}-2xy+{y}^{2}}· \frac{xy}{{x}^{2}+xy}+\frac{x}{x-y}\).(其中\(x = 1\),\(y = 2)\)

12.(2018•深圳)先化简,再求值:\((\frac{x}{{x – 1}} – 1) \div \frac{{{x^2} + 2x + 1}}{{{x^2} – 1}}\),其中\(x = 2\).

13.(2018•河南)先化简,再求值:\((\frac{1}{{x + 1}} – 1) \div \frac{x}{{{x^2} – 1}}\),其中\(x = \sqrt 2  + 1\).

14.(2018•玉林)先化简再求值:\((a – \frac{{2ab – {b^2}}}{a}) \div \frac{{{a^2} – {b^2}}}{a}\),其中\(a = 1 + \sqrt 2 \),\(b = 1 – \sqrt 2 \).

15.(2018•哈尔滨)先化简,再求代数式\((1 – \frac{1}{{a – 2}}) \div \frac{{{a^2} – 6a + 9}}{{2a – 4}}\)的值,其中\(a = 4\cos 30^\circ  + 3\tan 45^\circ \).

16.(2018•广元)先化简,再求值:\(\frac{a}{{a – 2}} \div (\frac{a}{{a – 2}} – \frac{{4a}}{{{a^2} – 4}})\),其中\(a = \sqrt 2  + 2\).

17.(2018•兰州)先化简,再求值:\((x – \frac{{3x – 4}}{{x – 1}}) \div \frac{{x – 2}}{{x – 1}}\),其中\(x = \frac{1}{2}\).

18.(2018•本溪)先化简,再求值:\((1 – \frac{4}{{a + 2}}) \div \frac{{{a^2} – 4a + 4}}{{2a – 4}}\),其中\(a = {2^{ – 1}} + {(\pi  – 2018)^0}\)

19.(2018•锦州)先化简,再求值:\((2 – \frac{{3x + 3}}{{x + 2}}) \div \frac{{{x^2} – 2x + 1}}{{x + 2}}\),其中\(x = 3\).

20.(2018•毕节市)先化简,再求值:\((\frac{{2a}}{{{a^2} – 4}} – \frac{1}{{a – 2}}) \div \frac{a}{{{a^2} + 4a + 4}}\),其中\(a\)是方程\({a^2} + a – 6 = 0\)的解.

21.(2018•赤峰)先化简,再求值:\(\frac{{{x^2}}}{{x + 1}} – x + 1\),其中\(x = \sqrt {12}  – {(\frac{1}{2})^{ – 1}} – |1 – \sqrt 3 |\).

22.(2018•抚顺)先化简,再求值:\((1 – x + \frac{3}{{x + 1}}) \div \frac{{{x^2} + 4x + 4}}{{x + 1}}\),其中\(x = \tan 45^\circ  + {(\frac{1}{2})^{ – 1}}\).

23.(2018•盘锦)先化简,再求值:\((1 – \frac{1}{{a – 1}}) \div \frac{{{a^2} – 4a + 4}}{{{a^2} – a}}\),其中\(a = 2 + \sqrt 2 \).

24.(2018•上海)先化简,再求值:\((\frac{{2a}}{{{a^2} – 1}} – \frac{1}{{a + 1}}) \div \frac{{a + 2}}{{{a^2} – a}}\),其中\(a = \sqrt 5 \).

25.(2018•资阳)先化简,再求值:\(\frac{{{a^2} – {b^2}}}{b} \div (\frac{{{a^2}}}{b} – a)\),其中\(a = \sqrt 2  – 1\),\(b = 1\).

26.(2018•广安)先化简,再求值:\(\frac{a}{{a + 1}} \div (a – 1 – \frac{{2a – 1}}{{a + 1}})\),并从\( – 1\),0,1,2四个数中,选一个合适的数代入求值.

27.(2018•烟台)先化简,再求值:\((1 + \frac{{{x^2} + 2}}{{x – 2}}) \div \frac{{x + 1}}{{{x^2} – 4x + 4}}\),其中\(x\)满足\({x^2} – 2x – 5 = 0\).

28.(2018•曲靖)先化简,再求值\((\frac{1}{{a – b}} – \frac{b}{{{a^2} – {b^2}}}) \div \frac{{{a^2} – ab}}{{{a^2} – 2ab + {b^2}}}\),其中\(a\),\(b\)满足\(a + b – \frac{1}{2} = 0\).

29.(2018•通辽)先化简\((1 – \frac{3}{{x + 2}}) \div \frac{{{x^2} – 2x + 1}}{{{x^2} – 4}}\),然后从不等式\(2x – 6 < 0\)的非负整数解中选取一个合适的解代入求值.

30.(2018•遵义)化简分式\((\frac{{{a^2} – 3a}}{{{a^2} – 6a + 9}} + \frac{2}{{3 – a}}) \div \frac{{a – 2}}{{{a^2} – 9}}\),并在2,3,4,5这四个数中取一个合适的数作为\(a\)的值代入求值.

31.(2018•长春)先化简,再求值:\(\frac{{{x^2} – 2}}{{x – 1}} + \frac{1}{{x – 1}}\),其中\(x = \sqrt 5  – 1\).

32.(2018•陕西)化简:\((\frac{{a + 1}}{{a – 1}} – \frac{a}{{a + 1}}) \div \frac{{3a + 1}}{{{a^2} + a}}\).

33.(2018•安顺)先化简,再求值:\(\frac{8}{{{x^2} – 4x + 4}} \div (\frac{{{x^2}}}{{x – 2}} – x – 2)\),其中\(|x| = 2\).

34.(2018•东莞市)先化简,再求值:\(\frac{2{a^2}}{a+4}· \frac{{a^2}-16}{{a^2}-4a}\),其中\(a = \frac{{\sqrt 3 }}{2}\).

35.(2018•菏泽)先化简,再求值:\((\frac{{{y^2}}}{{x + y}} – y) \div \frac{{x – y}}{{{x^2} – {y^2}}} – (x – 2y)(x + y)\),其中\(x =  – 1\),\(y = 2\).

36.(2018•恩施州)先化简,再求值:\(\frac{1}{{x^2}+2x+1}· (1+\frac{3}{x-1})\div \frac{x+2}{{x^2}-1}\),其中\(x = 2\sqrt 5  – 1\).

37.(2018•淮安)先化简,再求值:\((1 – \frac{1}{{a + 1}}) \div \frac{{2a}}{{{a^2} – 1}}\),其中\(a =  – 3\).

38.(2018•荆门)先化简,再求值:\((x + 2 + \frac{{3x + 4}}{{x – 2}}) \div \frac{{{x^2} + 6x + 9}}{{x – 2}}\),其中\(x = 2\sqrt 3 \).

39.(2018•湘潭)先化简,再求值:\((1 + \frac{4}{{x – 2}}) \div \frac{{x + 2}}{{{x^2} – 4}}\).其中\(x = 3\).

40.(2018•十堰)化简:\(\frac{1}{{a – 1}} – \frac{1}{{{a^2} + a}} \div \frac{{{a^2} – 1}}{{{a^2} + 2a + 1}}\)

41.(2018•娄底)先化简,再求值:\((\frac{1}{{x + 1}} + \frac{1}{{{x^2} – 1}}) \div \frac{x}{{{x^2} + 2x + 1}}\),其中\(x = \sqrt 2 \).

42.(2018•陇南)计算:\(\frac{b}{{{a^2} – {b^2}}} \div (\frac{a}{{a – b}} – 1)\)

43.(2018•南京)计算\((m + 2 – \frac{5}{{m – 2}}) \div \frac{{m – 3}}{{2m – 4}}\).

44.(2018•株洲)先化简,再求值:\(\frac{{x^2}+2x+1}{y}· (1-\frac{1}{x+1})-\frac{x^2}{y}\),其中\(x = 2\),\(y = \sqrt 2 \).

45.(2018•泸州)化简:\((1 + \frac{2}{{a – 1}}) \div \frac{{{a^2} + 2a + 1}}{{a – 1}}\).

46.(2018•常德)先化简,再求值:\((\frac{1}{{x + 3}} + \frac{6}{{{x^2} – 9}}) \div \frac{1}{{{x^2} – 6x + 9}}\),其中\(x = \frac{1}{2}\).

47.(2018•临沂)计算:\((\frac{{x + 2}}{{{x^2} – 2x}} – \frac{{x – 1}}{{{x^2} – 4x + 4}}) \div \frac{{x – 4}}{x}\).

48.(2018•聊城)先化简,再求值:\(\frac{a}{{a + 1}} – \frac{{a – 1}}{a} \div (\frac{a}{{a + 2}} – \frac{1}{{{a^2} + 2a}})\),其中\(a =  – \frac{1}{2}\).

49.(2018•眉山)先化简,再求值:\((\frac{{x – 1}}{x} – \frac{{x – 2}}{{x + 1}}) \div \frac{{2{x^2} – x}}{{{x^2} + 2x + 1}}\),其中\(x\)满足\({x^2} – 2x – 2 = 0\).

50.(2018•泰安)先化简,再求值\(\frac{{{m^2} – 4m + 4}}{{m – 1}} \div (\frac{3}{{m – 1}} – m – 1)\),其中\(m = \sqrt 2  – 2\).

2019.3.21




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