Question

$frac {4} {1+x} + frac {2} {1-x} >1$

Answer 1

$<var>frac{4}{1+x}+frac{2}{1-x}>1, \ frac{4}{1+x}+frac{2}{1-x}-1>0, \ frac{4(1-x)+2(1+x)-(1-x)(1+x)}{(1-x)(1+x)}>0, \ frac{4-4x+2+2x-1+x^2}{(1-x)(1+x)}>0, \ frac{x^2-2x+5}{(1-x)(1+x)}>0, \ (x^2-2x+5)(1-x)(1+x)>0, \ (x^2-2x+5)(1-x)(1+x)=0, \ x^2-2x+5=0, D=-16<0, a=1>0, x^2-2x+5>0, \ 1-x=0, x_1=1, \ 1+x=0, x_2=-1, \ (1-x)(1+x)>0, \ -(x-1)(x+1)>0, \ (x-1)(x+1)<0, \ -1<x<1< var=$

x∈(-1;1)