Question

初高中衔接的一道数学题解不等式:1/(x+4)+1/(x+5)>1/(x+6)+1/(x+3)

Answer 1

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