Question

Inequação em U = R. ---->>> a) X^2+ 2X -1/ X^2 -1 >_ ( maior ou igual) 1/ X + 1. Se alguém souber, por favor respondam.

Answer 1

$\frac{x² +2x -1}{x² -1}$≥$\frac{1}{x+1}$


mmc= (x+1)(x-1)

x² +2x -1≥ x -1
 
x² +x -1 +1≥0

x²+x≥0

x( x+1)≥0

x≥0      e      x+1≥0
                       x≥ -1

S= {x∈R/x≥-1}

Answer 2

$\frac{x^2+2x-1}{x^2-1}\geq\frac{1}{x+1}\\\\\frac{x^2+2x-1}{x^2-1}-\frac{1}{x+1}\geq0\\\\\frac{x^2+2x-1}{x^2-1/1}-\frac{1}{x+1/(x-1)}\geq0\\\\\frac{x^2+2x-1-x+1}{x^2-1}\geq0\\\\\frac{x^2+x}{x^2-1}\geq0\\\\\frac{x(x+1)}{(x+1)(x-1)}\geq0$
 
 Quadro de sinais:

___+___[-1]___-______[0]__+_________+__
___+___(-1)___-__________-____(+1)__+____
___+___(-1)___+______[0]__-____(+1)__+_____


$\boxed{S=\left\{x\in\mathbb{R}|x<-1\vee\,-1<x\leq0\vee\,x>1,x\neq-1\right\}}$