Question

Giải câu 1 giùm 1

Answer 1

1/x-1>=1/x+1+1

=>\(\dfrac{1}{x-1}>=\dfrac{1}{x+1}+1=\dfrac{1+x+1}{x+1}=\dfrac{x+2}{x+1}\)

=>\(\dfrac{1}{x-1}-\dfrac{x+2}{x+1}>=0\)

=>\(\dfrac{x+1-\left(x+2\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}>=0\)

=>\(\dfrac{x+1-x^2+x-2x+2}{\left(x-1\right)\left(x+1\right)}>=0\)
=>\(\dfrac{-x^2+3}{\left(x-1\right)\left(x+1\right)}>=0\)

=>\(\dfrac{x^2-3}{x^2-1}< =0\)

=>1<x^2<=3

=>1<x=căn 3 hoặc -1>x>=-căn 3