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专题04 分式及其运算解读考点知识点名师点晴分式的概念整式A除以整式B，可以表示成 的形式，如果除式B中含有字母，那么称 为分式若B0，则 有意义；若B=0，则 无意义；若A=0且B0，则 0. 分式的基本性质及应用1.分式的基本性质 要熟练掌握，特别是乘或除以的数不能为02.分式的变号法则分式的分子、分母与分式本身的符号，改变其中任何两个，分式的值不变.3.分式的约分、通分通分与约分的依据都是分式的基本性质4.最简分式分子与分母没有公因式 分式的运算1.分式的加减法异分母的分式相加减，要先通分，然后再加减2.分式的乘除法、乘方熟练应用法则进行计算3.分式的混合运算应先算乘方，再将除法化为乘法，进行约分化简，最后进行加减运算若有括号，先算括号里面的灵活运用运算律，运算结果必须是最简分式或整式2年中考【2015年题组】1（2015常州）要使分式有意义，则x的取值范围是（）A B C D【答案】D【解析】试题分析：要使分式有意义，须有，即，故选D考点：分式有意义的条件2（2015济南）化简的结果是（）A B C D【答案】A考点：分式的加减法3（2015百色）化简的结果为（）A B C D【答案】C【解析】试题分析：原式=故选C考点：分式的加减法4（2015甘南州）在盒子里放有三张分别写有整式a+1，a+2，2的卡片，从中随机抽取两张卡片，把两张卡片上的整式分别作为分子和分母，则能组成分式的概率是（）A B C D【答案】B【解析】试题分析：分母含有字母的式子是分式，整式a+1，a+2，2中，抽到a+1，a+2做分母时组成的都是分式，共有32=6种情况，其中a+1，a+2为分母的情况有4种，所以能组成分式的概率=故选B考点：1概率公式；2分式的定义；3综合题5（2015龙岩）已知点P（a，b）是反比例函数图象上异于点（1，1）的一个动点，则=（）A2 B1 C D【答案】B考点：1反比例函数图象上点的坐标特征；2分式的化简求值；3条件求值6（2015山西省）化简的结果是（）A B C D【答案】A【解析】试题分析：原式=，故选A考点：分式的加减法7（2015泰安）化简：的结果等于（）A B C D【答案】B【解析】试题分析：原式=故选B考点：分式的混合运算8（2015莱芜）甲乙两人同时从A地出发到B地，如果甲的速度v保持不变，而乙先用v的速度到达中点，再用2v的速度到达B地，则下列结论中正确的是（）A甲乙同时到达B地 B甲先到达B地C乙先到达B地 D谁先到达B地与速度v有关【答案】B考点：1列代数式（分式）；2行程问题9（2015内江）已知实数a，b满足：，则|= 【答案】1【解析】试题分析：，两式相减可得，即，=1故答案为：1考点：1因式分解的应用；2零指数幂；3条件求值；4综合题；5压轴题10（2015黄冈）计算的结果是_【答案】【解析】试题分析：原式=故答案为：考点：分式的混合运算11（2015安徽省）已知实数a、b、c满足ababc，有下列结论：若c0，则；若a3，则bc9；若abc，则abc0；若a、b、c中只有两个数相等，则abc8其中正确的是 （把所有正确结论的序号都选上）【答案】考点：1分式的混合运算；2解一元一次方程12（2015梅州）若，对任意自然数n都成立，则 ， ；计算： 【答案】；【解析】试题分析：=，可得，即：，解得：a=，b=；m=，故答案为：；考点：1分式的加减法；2综合题13（2015河北省）若，则的值为 【答案】【解析】试题分析：，原式=，故答案为：考点：分式的化简求值14（2015绥化）若代数式的值等于0，则x=_【答案】2【解析】试题分析：由分式的值为零的条件得，2x60，由，得x=2或x=3，由2x60，得x3，x=2，故答案为：2考点：分式的值为零的条件15（2015崇左）化简：【答案】考点：分式的混合运算16（2015桂林）先化简，再求值：，其中【答案】，【解析】试题分析：分解因式后，利用除法法则变形，约分得到最简结果，把x的值代入计算即可求出值试题解析：原式=，当时，原式=考点：分式的化简求值17（2015南京）计算：【答案】【解析】试题分析：首先将括号里面通分运算，进而利用分式的性质化简求出即可试题解析：原式=考点：分式的混合运算18（2015苏州）先化简，再求值：，其中【答案】，考点：分式的化简求值19（2015盐城）先化简，再求值：，其中a=4【答案】，4【解析】试题分析：根据分式混合运算的法则把原式进行化简，再求出x的值代入进行计算即可试题解析：原式=；当a=4时，原式=4考点：分式的化简求值20（2015成都）化简： 【答案】【解析】试题分析：括号内先通分，同时把除法转化为乘法，再用分式乘法法则计算机即可试题解析：原式=考点：分式的加减法 21（2015资阳）先化简，再求值：，其中x满足【答案】，考点：1分式的混合运算；2分式的化简求值22（2015达州）化简，并求值，其中a与2、3构成ABC的三边，且a为整数【答案】，1【解析】试题分析：原式第一项约分后，两项通分并利用同分母分式的减法法则计算得到结果，把a的值代入计算即可求出值试题解析：原式=，a与2、3构成ABC的三边，且a为整数，1a5，即a=2，3，4，当a=2或a=3时，原式没有意义，则a=4时，原式=1考点：1分式的化简求值；2三角形三边关系23（2015广元）先化简：，然后解答下列问题：（1）当时，求原代数式的值；（2）原代数式的值能等于吗？为什么？【答案】（1）2；（2）不能考点：分式的化简求值24（2015凉山州）先化简：，然后从的范围内选取一个合适的整数作为x的值代入求值【答案】；当x=2时，原式=0，当x=2时，原式=8【解析】试题分析：原式括号中两项通分并利用同分母分式的减法法则计算，同时根据除法法则变形，约分得到最简结果，将x=0代入计算即可求出值试题解析：原式=，满足的整数有2，1，0，而x=1，0时，原式无意义，x=2，当x=2时，原式=，当x=2时，原式=考点：分式的化简求值25（2015广州）已知A=（1）化简A；（2）当x满足不等式组，且x为整数时，求A的值【答案】（1）；（2）1考点：1分式的化简求值；2一元一次不等式组的整数解26（2015白银）有三张卡片（形状、大小、颜色、质地都相等），正面分别下上整式，3将这三张卡片背面向上洗匀，从中任意抽取一张卡片，记卡片上的整式为A，再从剩下的卡片中任意抽取一张，记卡片上的整式为B，于是得到代数式（1）请用画树状图或列表的方法，写出代数式所有可能的结果；（2）求代数式恰好是分式的概率【答案】（1）答案见试题解析；（2）【解析】试题分析：（1）画出树状图，由树状图即可求得所有等可能的结果；（2）由（1）中的树状图，可求得抽取的两张卡片结果能组成分式的情况，利用概率公式求解即可求得答案试题解析：（1）画树状图：（2）代数式所有可能的结果共有6种，其中代数式是分式的有4种，所以P （是分式）=考点：1列表法与树状图法；2分式的定义【2014年题组】1（2014年无锡中考） 分式可变形为（ ）A. B. C. D. 【答案】D考点：分式的基本性质2.（2014年杭州中考）若，则w=（ ）A. B. C. D. 【答案】D【解析】试题分析：，w=故选D考点：分式的化简3.（2014年温州中考）要使分式有意义，则x的取值应满足（ ）A. B. C. D. 【答案】A【解析】试题分析：根据分式分母不为0的条件，要使在实数范围内有意义，必须故选A考点：分式有意义的条件4.（2014年牡丹江中考）若x：y=1：3，2y=3z，则的值是（）A5BCD5【答案】A【解析】试题分析：x：y=1：3，设x=k，y=3k，2y=3z，z=2k，故选A考点：比例的性质5.（2014年凉山中考）分式的值为零，则x的值为（ ）A. 3 B. 3 C. 3 D. 任意实数【答案】A考点：分式的值为零的条件6.（2014年常德中考）计算： 【答案】【解析】试题分析：原式=.考点：分式的加减法7.（2014年河池中考）计算： 【答案】1【解析】试题分析：根据分式加减法运算法则直接计算：考点：分式加减法8.（2014年镇江中考）化简：【答案】考点：分式的混合运算9.（2014年苏州中考）先化简，再求值：，其中【答案】【解析】试题分析：先将括号里面的通分后，将除法转换成乘法，约分化简. 然后代x的值，进行二次根式化简试题解析：原式=当时，原式=考点：1.分式的化简求值；2. 二次根式化简10.（2014年抚顺中考）先化简，再求值：（1-），其中x=（+1）0+（）-1tan60【答案】2+2【解析】试题分析：原式括号中两项通分并利用同分母分式的减法法则计算，同时利用除法法则变形，约分得到最简结果，利用零指数幂、负指数幂法则以及特殊角的三角函数值求出x的值，代入计算即可求出值试题解析：原式=，x=（+1）0+（）-1tan60=1+2，当1+2时，原式=2+2考点：1.分式的化简求值；2.零指数幂；3.负整数指数幂；4.特殊角的三角函数值考点归纳归纳 1：分式的有关概念基础知识归纳： 分式有意义的条件是分母不为零；分式无意义的条件是分母等于零；分式值为零的条件是分子为零且分母不为零注意问题归纳：分式有意义的条件是分母不为0，无意义的条件是分母为0分式值为0要满足两个条件，分子为0，分母不为0【例1】使分式有意义，则x的取值范围是（）x1Bx=1Cx1Dx1【答案】A【解析】根据题意得：x-10，解得：x1故选A考点：分式的有关概念【例2】分式的值为零，则x的值为（ ）A. 3 B. 3 C. 3 D. 任意实数【答案】A考点：分式的有关概念归纳2：分式的性质基础知识归纳： 分式的分子与分母都乘以（或除以）同一个不等于零的整式，分式的值不变用式子表示为 注意问题归纳：分式的基本性质是分式变形的理论依据，所有分式变形都不得与此相违背，否则分式的值改变；将分式化简，即约分，要先找出分子、分母的公因式，如果分子、分母是多项式，要先将它们分别分解因式，然后再约分，约分应彻底；巧用分式的性质，可以解决某些较复杂的计算题，可应用逆向思维，把要求的算式和已知条件由两头向中间凑的方式来求代数式的值【例3】化简的结果是（ ）BCD【答案】D考点：分式的性质【例4】已知x+y=xy，求代数式-（1-x）（1-y）的值【答案】0【解析】x+y=xy，-（1-x）（1-y）=-（1-x-y+xy）=-1+x+y-xy=1-1+0=0考点：分式的性质归纳 3：分式的加减运算基础知识归纳：加减法法则： 同分母的分式相加减：分母不变,分子相加减 异分母的分式相加减：先通分,变为同分母的分式,然后再加减 注意问题归纳：1.分式加减运算的运算法则：同分母分式相加减，分母不变，分子相加减；异分母分式相加减，先通分，变为同分母的分式，然后再加减异分母分式通分的依据是分式的基本性质，通分时应确定几个分式的最简公分母.求最简公分母的方法是：将各个分母分解因式；找各分母系数的最小公倍数；找出各分母中不同的因式，相同因式中取次数最高的，满足的因式之积即为各分式的最简公分母【例5】计算：的结果是 【答案】【解析】考点：分式的加减法【例6】化简的结果是 【答案】考点：分式的加减法归纳 4：分式的乘除运算基础知识归纳:1.乘法法则：分式乘分式,用分子的积作为积的分子,分母的积作为积的分母.乘方法则：分式的乘方,把分子、分母分别乘方2.除法法则：分式除以分式,把除式的分子、分母颠倒位置后与被除式相乘注意问题归纳：分式乘除法的运算与因式分解密切相关，分式乘除法的本质是化成乘法后，约去分式的分子分母中的公因式，因此往往要对分子或分母进行因式分解（在分解因式时注意不要出现符号错误），然后找出其中的公因式，并把公因式约去【例7】计算：【答案】x【解析】原式考点：分式的乘除法归纳5：分式的混合运算基础知识归纳：在分式的混合运算中，应先算乘方，再将除法化为乘法，进行约分化简，最后进行加减运算若有括号，先算括号里面的灵活运用运算律，运算结果必须是最简分式或整式注意问题归纳：注意运算顺序，计算准确【例8】化简：【答案】考点：分式的混合运算1年模拟1（2015届四川省成都市外国语学校中考直升模拟）要使有意义，则x应满足（ ）Ax3 Bx3且x Cx3 Dx3【答案】D【解析】试题分析：由题意得，解不等式得，x3，解不等式的，x，所以，x3故选D考点：1二次根式有意义的条件；2分式有意义的条件2（2015届山东省威海市乳山市中考一模）计算（-）-1=（ ）A- B C-2 D2【答案】C【解析】试题解析：故选C考点：负整数指数幂3（2015届山东省潍坊市昌乐县中考一模）分式的值为0，则（ ）Ax=-1 Bx=1 Cx=1 Dx=0【答案】B考点：分式的值为零的条件4（2015届广东省深圳市龙华新区中考二模）化简的结果是（ ）A-1 B1 C1+x D1-x【答案】A【解析】试题分析：原式=故选A考点：分式的加减法5（2015届江苏省南京市建邺区中考一模）计算a3（）2的结果是（ ）Aa Ba5 Ca6 Da8【答案】A【解析】试题分析：原式=a3=a，故选A考点：分式的乘除法6（2015届河北省中考模拟二）已知a=，b=，则（）的值为（ ）A1 B C D【答案】B考点：分式的化简求值7（2015届北京市平谷区中考二模）分式有意义的条件是 【答案】a2【解析】试题分析：根据分式有意义的条件可知分母a-20，所以a2考点：分式有意义的条件8（2015届山东省聊城市中考模拟）若与（x+1）0都有意义，则x的取值范围为 【答案】x-1且x1【解析】试题分析：根据题意得：解得：x-1且x1故答案为：x-1且x1考点：1二次根式有意义的条件；2分式有意义的条件；3零指数幂9（2015届广东省佛山市初中毕业班综合测试）若分式的值为零，则x的值为 【答案】x=-1【解析】试题分析：根据题意，得|x|-1=0，且x-10，解得x=-1故答案为：x=-1考点：分式的值为零的条件10（2015届江苏省南京市建邺区中考一模）在函数y=中，自变量x的取值范围是 【答案】x1【解析】试题分析：根据题意得1-x0，解得x1故答案为：x1考点：1函数自变量的取值范围；2分式有意义的条件11（2015届北京市门头沟区中考二模）已知，求的值【答案】1-考点：分式的化简求值12（2015届四川省成都市外国语学校中考直升模拟）计算题（1）先化简，再求值：，其中a=sin45，b=cos30；（2）若关于x的方程无解，求a的值【答案】（1） ；（2） a=1【解析】试题分析：（1）原式第二项利用除法法则变形，约分后利用同分母分式的减法法则计算，约分得到最简结果，把a与b的值代入计算即可求出值；（2）分式方程去分母转化为整式方程，由分式方程无解求出x的值，代入计算即可求出a的值试题解析：（1）原式=-（a-b）=，当a=sin45=，b=cos30=时，原式=；（2）去分母得：x2-ax-3x+3=x2-x，解得：x=，由分式方程无解，得到x（x-1）=0，即x=0或x=1，若x=0，a无解；若x=1，解得：a=1考点：1分式的化简求值；2分式方程的解；3特殊角的三角函数值13（2015届安徽省安庆市中考二模）先化简，再求值：（），其中x=【答案】，1考点：分式的化简求值14（2015届山东省威海市乳山市中考一模）化简代数式，并判断当x满足不等式组时该代数式的符号【答案】负号【解析】试题分析：做除法时要注意先把除法运算转化为乘法运算，而做乘法运算时要注意先把分子、分母能因式分解的先分解，然后约分化简为；再分别求出一元一次不等式组中两个不等式的解，从而得到一元一次不等式组的解集，依此分别确定x+10，x+20，从而求解试题解析：原式=；不等式组，解不等式，得x-1解不等式，得x-2，不等式组的解集是-2x-1，当-2x-1时，x+10，x+20，0，即该代数式的符号为负号考点：1分式的化简求值；2解一元一次不等式组15（2015届山东省日照市中考模拟）先化简，再求值：，其中，【答案】-4考点：分式的化简求值16（2015届湖北省黄石市6月中考模拟）先化简再求值，已知a2+2a7=0【答案】，考点：分式的化简求值（英文版 ） easily blame, to prevent the broken window effect. Supervise the leading cadres to play an exemplary role, take the lead in the strict implementation of the and , lead to safeguard the solemnity and authority of the party discipline, ensure that the party discipline and the laws and regulations for implementation in place. Throughout the discipline in the daily supervision and management, strengthen supervision and inspection, from the thorough investigation of violations of discipline behavior. Strengthen to key areas, key departments and key projects as well as the masses reflect the concentration of the units and departments for supervision. - strengthening supervision, discipline inspection and supervision of cadres to set an example for compliance with the and is a man must be hexyl, blacksmith needs its own hardware. Discipline inspection organs as the executor of the party discipline, and supervisor of the defenders, for its supervision must be more strictly, discipline inspection and supervision of cadres to firmly establish the awareness of Party Constitution, sense of discipline and rules consciousness, politics loyalty, sense obey. Action speak Ji Ordinance to set an example of the regulations of the rule of law, strengthen supervision and accept the supervision of the firmness and consciousness, do comply with and . To firmly establish the discipline must first be disciplined, the supervisor will be subject to the supervision of concept, and consciously safeguard and implement party compasses party, take the lead in practicing three strict real strict, so loyal, clean, play. To be good at learning, the Constitution and the as morality, politics and brought to fruition; to implement , do not want to, dare not, not with disciplinary ruler to supervision; to discipline a ruler, often the control inspection, and consciously in the ideological red line to draw the row Ming Good accumulation is indeed the bottom line, so that the heart has fear, said to have quit, the line has ended. Attached: indifferent to heart, calmly to the table in our life, there are many unpredictable things will happen, some good, some bad things, we cannot control is powerless to stop, but with time, you will find in life sometimes turns out to be not good, some bad things finally turned out to be a good thing, but then we muddy however did not know, this is the life teach us things. 1, life can be complex, can also be simple. Want simple life of precipitation, to have enough time to reflect, to make Become more perfect. Life is the most important thing is not to win, but the struggle; not to have conquered, but to have fought well. 2, the plain is the background of life. Live a plain life, give up on themselves is not a coward, but the wise answers; not disillusioned after the heart, such as ashes, but experience the storm after the enlightenment; not unrewarding perfunctorily, but calm attitude of life of unrestrained self-confidence. Plain living, there is no noise noisy, no earthly troubles, more did not fill in the discontent of desire, some just a calm, a calm. 3, memory of heart will not good things to erase the, life is a When no movie, pain is a beginning, the struggle is a kind of process, death is a kind of ending. Give up this giving up is the helpless, do not give up the abandoned, do not give up this giving up is ignorance, do not give up should not give up is persistent. 4, a thing figured is heaven, think impassability is hell. Since the living, to live better. Sometimes we because of too narrow-minded, too care around the chores and penny wise and pound foolish, not worth the candle. Some things to attract trouble and worry, completely depends on how we look at and deal with it. Dont always take everything back to things, and dont get into a blind alley, dont want to face, dont be narrow-minded. Poke to care, is a kind of open-minded, a free and easy. 5, I am not afraid of others behind me a knife, I afraid to look back and see stab me, is my intention to treat people; I am not afraid of the truth to tell the best friend, Im afraid he turned to it as a joke to tell dont 6, when we are in a positive frame of mind, you will find many good things; and when we are in a negative state of mind, you will find many depressed things; life happy and worry, all is you of life attitude, optimistic, good luck; loss of sink, Eritrea company. When you are in adversity, may wish to change a point of view to think everything over to the good Think, because good mentality decided the fate of the! 7, people are tired, rest; heart tired, calm. Grow up, mature, this society read. Tired and sad, squat down, to their a hug. Because the world no one can sympathize with you, have mercy on you. You cry, tears is your own; you pain, no one can understand. Then you only tears to smile. 8, each people have youth,Each youth are a story, the life of the world never gets easier, I want what, wish the world all know, as has been the same; now want anything, for fear that others know, or like to lose the same. 9, the heart move, everything in the world is followed by birth, Rangrang, important thing is often the most difficult to open ones mouth, because words will reduce its importance; to let strangers people care about your life in the good things, the original is not easy 10, do not blame, do not laugh at who, also dont envy who. Like a person is a kind of feeling, not like a person is true. The truth is easy to explain, I feel Is unspeakable. The best travel life is that you in a strange place found a long lost touched. 11, happy life not in the bustling in, and in the peace of mind; no matter how many grievances, how uncomfortable, and ultimately to heal themselves or their own, others may got you to comfort, but never know your heart is how wanjianchuanxin. 12, maam, like a movie, learn to appreciate, learn to be grateful, learn tolerance, and goodness, helping others. Instead of accusing the society, as into one; and an exception is better to give than to what 13, dont envy him A sum of, dont lose your life and the life, respectively is: the former is a we experienced cannot escape in a day finally will last minute, while the latter is our persistent, we want to cherish the memory of those people and things. 14, learn to smile, learn to strong, the world you know so many people, so many people and you are, you cannot change also cant let everyone like you, so also do not want to do. Life is too short to go crazy to love to go to waste, to chase the dream to regret. 15, when temper, a blessing to go. A wounding elegant people, the key is to control their own emotions. With the mouth is the most stupid behavior. A control negative emotions than a can take a city more powerful water flow slow, language is expensive. People spent two years of time to learn to speak, but to spend a few years time to shut up. That is a kind of ability, that is a kind of wisdom. 16, life is not perfect, sometimes, growth is not a cry, not an eyeful of tears, there is no trace of emotion, there is no gleam of hope, no desire, no action, no static, there is only one kind of downward sinking feeling, sink A murky? 6? 7? 6? 7 sink? 6? 7? 6? 7 toward the bottom of the sink. 17, in some way, do not go, you will not know the other side scenery is beautiful. To you is not good, you do not mind too much, no one has an obligation to you; you learn knowledge, is you have weapons, you can start from scratch, but not unarmed; how do you treat people, does not represent how others treat you, if cannot see through this point, only inviting worry. 18, time is like a sponge in the water, as long as you are willing to squeeze, the total water is still there. Every life, after the ups and downs The best test of live, to life, survival and continuation, do not stop the struggle in the joys and sorrows of life on the road, so that different soul to bear life beat, acceptance of suffering. 19, indifferent to heart, calmly in table, elegant and comfortable life, do not take what is so important. The pursuit will be disappointed; to be alive, you will have trouble. Life is the most afraid of what all want to care about, but also what all grasp is not firm, without scenery, separated populations, such as not to desire, all docked in the fate of the end. Why is too rigid, the natural, to go stay not to live, let go of obsession, revel is 20, if the fate of the broken Hopes of sailing, please dont despair, the coast is still, if the fate of the withered petals of the beautiful, please do not sink, the spring is still, life will always be endless trouble, please dont helpless, because they are still alive, is still a dream, the sun still, we still. Lost, keep memories; to get, must work to; but the most important is good to cherish their own. 21, life, select the complex, is to choose the pain; choose a simple, is choose to be happy. The complex world like aSignificance of pride. Hope is the ornate palace, outside people admiring the magnificent, living in the deep knowledge of living it to pay the price. Simple world as a simple log cabin outside ridiculed shabby, the heart is willing to go live to know the joy. Suffering and joy is their own choice. 22, learn how to use a single powerful heart, let the past be the past, let the future come. Life is really the end of the end of an eagle is flying wings, life is constantly pursuit. Dont miss to regret, dont wait for old just miss. Time to return, seize every moment, again painstakingly again tired also Those struggling to fly. 23, life could not Yimapingchuan, even flat pavement, inevitably there will be a few pieces of roadblocks. Some of the rocks around the past, while others have to move it out. Just move others put the stone is very easy, because the stone from the appearance we can discern; difficult to myself to move away the heart of stone head. Leave time to spend with her, often reflect my heart, so as to remove your heart of stone. 24, everything does not have to be demanding, come to, everything does not have to care about, over the past; failing to do not frown, laugh it laugh. Results Dont demand, do to; life is a simple, calm and peaceful. Always not to choose their own path and regret, life is like a train, the scenery and then the United States will retreat, the passage of time and encounter will eventually drifting further and further away, before is always himself. 25, everyone has a weakness, weakness is true humanity. That has no weakness, a shallow person. That people think there is no weakness, mostly false. Life has shortcomings, there are shortcomings is the real life. That no one regret, or childish or numbness or Self deception. It is in tolerance of weakness and so on to accept, people live happily.Hello, everyone! I am a party member. The title of my speech is: study and implement the partys two laws, doing practical play highway. 2015 October 18, the Central Committee of the Communist Party of China promulgated the implementation of the and Chinese Communist Party discipline and punishment regulations. We Heyuan male passers-by to respond p
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