分式不等式与一元高次不等式的解法训练

分式不等式与一元高次不等式的解法训练 【知识点梳理】 一、一元高次不等式 方法:先因式分解,再使用穿根法. 注意:因式分解后,整理成每个因式中未知数的系数为正. 使用方法: 等号不成立的根要标虚点. ?在数轴上标出化简后各因式的根,使等号成立的根,标为实点,?自右向左自上而下穿线,遇偶次重根不穿透,遇奇次重根要穿透(叫奇穿偶不穿). ?数轴上方曲线对应区域使“>”成立, 下方曲线对应区域使“<”成立. 二、分式不等式 方法1:利用符号法则转化为一元一次不等式组，进而进行比较。 方法2:在分母不为0的前提下，两边同乘以分母的平方。 通过例1，得出解分式不等式的基本思路:等价转化为整式不等式(组): ,fxgx,,0，，，，fxfx，，，，,(1) (2) ,,,,00fxgx,,0，，，，,gxgx，，，，gx,0，，,,解题方法:数轴标根法。 解题步骤:(1)首项系数化为“正”;(2)移项通分，不等号右侧化为“0”;(3)因式分解， 化为几个一次因式积的形式;(4)数轴标根。 xaxa？xa,,,，，，，，，12m，，归纳:分式不等式主要是转化为,0或,0，再用数轴标根法，，，，，，xbxb？xb,,,12n 求解。 【典型例题】 例1、解不等式 32(1)2x-x-15x,0; 24(2)(x+4)(x+5)(2-x),0( 例2、解下列不等式: 2? (x+1)(x-1)(x-2)(x-3)>0; ? (x+2)(x+x+1)>0; 22? (x+2)(x+1)<0; (4)(x+2)(x+1)0; , 22(5) (x-1)(x-5x-6)> 0 例3、解下列不等式: 2222?(x-1)(x-1)(x-x-2)<0; ?(x+1)(x-2)(x-1)0; ?, 22(x-1)(x-x-2)0; , 2xx,，32,0例4、解不等式: 2,，,xx712 2xx,，911,7、解不等式:例5 2xx,，21 regulations, construction scaffolding is safe and reliable, and climbing ladders, lifting Commander 1 established, full-time safety officer 1, responsible for checking the safety guarantee measures, echoed up and down, prevent accidents. 12) traffic pavement in accordance with requirements of the transport sector, and separated by closed isolation barrier, construction and non-construction with barrier isolation. 13) volunteer fire organizations, employees conducting fire prevention publicity and education of the knowledge, skills, and organizational implementation of fire-fighting and emergency evacuation plans and walkthroughs. 8.4.5 specific construction program for safety technology according to the Hebei provincial construction safety inspection rules for the implementation of requirements of the standard, a separate specific construction program for the following 1) scaffold erection, dismantling programme; 2) Foundation support schemes; 3) construction project of template engineering; 4) "three treasures", "four" protection scheme; 5) construction organization design of temporary power supply; 6) installation, demolition of a tower crane programme; 7) lifting operation plan. 8.5 8.5.1 environmental management goals of environmental protection, civilization construction without major environmental pollution accident, waste gas, waste water, noise, dust, solid 2xx，,56例6、解不等式: ,02xx,，32 2121xx，，例7、解不等式: ,xx,,332 23,x例8、解不等式:(不能十字相乘分解因式;无法分解因式) ,32xx，，1 例9、解下列不等式。 118,2x?x+2+>7+; ?1; ,x,10x,10x,3x，2 23(x，1)(x,1)(x,2)(3x,2)(x,2)(2x，2)(x,2)?< ; ?0。 ,22456(x,4)(x,4)(x,3)(x,4)(x,5) 【巩固练习】 1、解下列不等式: 2?(x+1)(x-1)(x-4)>0; 23 ?(x+2)(x+1)(x-1)(x-3)>0 ; 23?(x+2)(x+1)(x-1)(3-x))0 , 22?(x-1)(x-1)(x-x-2)0; , regulations, construction scaffolding is safe and reliable, and climbing ladders, lifting Commander 1 established, full-time safety officer 1, responsible for checking the safety guarantee measures, echoed up and down, prevent accidents. 12) traffic pavement in accordance with requirements of the transport sector, and separated by closed isolation barrier, construction and non-construction with barrier isolation. 13) volunteer fire organizations, employees conducting fire prevention publicity and education of the knowledge, skills, and organizational implementation of fire-fighting and emergency evacuation plans and walkthroughs. 8.4.5 specific construction program for safety technology according to the Hebei provincial construction safety inspection rules for the implementation of requirements of the standard, a separate specific construction program for the following 1) scaffold erection, dismantling programme; 2) Foundation support schemes; 3) construction project of template engineering; 4) "three treasures", "four" protection scheme; 5) construction organization design of temporary power supply; 6) installation, demolition of a tower crane programme; 7) lifting operation plan. 8.5 8.5.1 environmental management goals of environmental protection, civilization construction without major environmental pollution accident, waste gas, waste water, noise, dust, solid 4?x+1 ,x，1 23x,14x，14?1; ,2x,6x，8 2x，12x，1?>; x,33x,2 2(x,1)(x，2)?0; ,(x,3)(x,4) 2:解不等式: x,321x,1、 2、 ,0,12,xx，3 22xx,，32xx,,21,0,03、 4、 2xx,,23x,2 32xxx,，，16，，xx,3，，，，,05、 6、 ,0229,xx，3，， regulations, construction scaffolding is safe and reliable, and climbing ladders, lifting Commander 1 established, full-time safety officer 1, responsible for checking the safety guarantee measures, echoed up and down, prevent accidents. 12) traffic pavement in accordance with requirements of the transport sector, and separated by closed isolation barrier, construction and non-construction with barrier isolation. 13) volunteer fire organizations, employees conducting fire prevention publicity and education of the knowledge, skills, and organizational implementation of fire-fighting and emergency evacuation plans and walkthroughs. 8.4.5 specific construction program for safety technology according to the Hebei provincial construction safety inspection rules for the implementation of requirements of the standard, a separate specific construction program for the following 1) scaffold erection, dismantling programme; 2) Foundation support schemes; 3) construction project of template engineering; 4) "three treasures", "four" protection scheme; 5) construction organization design of temporary power supply; 6) installation, demolition of a tower crane programme; 7) lifting operation plan. 8.5 8.5.1 environmental management goals of environmental protection, civilization construction without major environmental pollution accident, waste gas, waste water, noise, dust, solid