當(dāng)x<0時(shí)1/x<0<1 恒成立
當(dāng)x=0 分母不能為0
當(dāng)x>0時(shí)不等式兩邊同時(shí)乘以x,不等式不改變方向,得1
x<0或x>1
2.(x-1)分之(4x+3)>5
1)當(dāng)x<1時(shí)不等式兩邊同時(shí)乘以x-1,不等式改變方向
得4x+3<5(x-1)
==>x>8 這與x<1相矛盾
2)x=1 x-1=0 分母不能為0
3)當(dāng)x>1時(shí)不等式兩邊同時(shí)乘以x-1,不等式不改變方向
得4x+3>5(x-1)
==>x<8
故1
1) 當(dāng)x<0或x>3時(shí)不等式兩邊同時(shí)乘以x(x-3),不等式不改變方向
得2(x-3)<2x
-6<0
恒成立
2)當(dāng)0
-6>0
恒不成立
3)當(dāng)x=0或x=3時(shí)分母為0,不成立
綜合以上幾點(diǎn)得
x<0或x>3
4.(x-4)分之1小于等于1-(4-x)分之x
1/(x-4)<=1-x/(4-x)
==>1/(x-4)+x/(4-x)-1<=0
==>1/(x-4)-x/(x-4)-1<=0
==>(1-x-x+4)/(x-4)<=0
==>(5-2x)/(x-4)<=0
==>(2x-5)/(x-4)>=0
==>x>4或x<=5/2