1/(x+4)+1/(x+5)>1/(x+6)+1/(x+3)
1/(x+5)-1/(x+6)>1/(x+3)-1/(x+4)
1/(x+5)(x+6)>1/(x+3)(x+4)
由不等式x≠,﹣3,﹣4,﹣5,﹣6
①当x﹤﹣4,x﹥﹣3,且x≠﹣5,﹣6时
等式两边同号,则
(x+3)(x+4)﹥(x+5)(x+6)
x*x+7x+12﹥x*x+11x+30
4x﹤﹣18
x﹤﹣4.5
则x﹤﹣4.5且x≠﹣5,﹣6
②当﹣4﹤x﹤﹣3时,
不等式左端为正右端为负,不等式成立,
由①②得﹣4﹤x﹤﹣3, x﹤﹣4.5且x≠﹣5,﹣6