besoin d’aide pour cet exercice svp !!!!

Réponse :

Explications étape par étape

Bonsoir

1)(2x - 1)/(x + 1) + 2 =

= (2x - 1)/(x + 1) + 2(x + 1)/(x + 1)

= (2x - 1 + 2x + 2)/(x + 1)

= (4x + 1)/(x + 1)

2) tableau de signe de (2x - 1)/(x + 1)

2x - 1 = 0

2x = 1

x = 1/2

x..........|-inf...............(-1)..............(1/2)...........+inf

2x-1....|.........(-)..................(-).........o......(+)...........

x+1......|.........(-)..........||......(+)................(+)...........

Eq.......|.........(+).........||......(-)..........o.....(+)...........

3) résoudre :

(2x - 1)/(x + 1) [tex]\ge -2[/tex]

(4x + 1)/(x + 1) [tex]\ge[/tex] 0

4x + 1 = 0

4x = -1

x = -1/4

x...........|-inf.............(-1).............(-1/4)...........+inf

4x+1.....|.........(-)..............(-)..........o......(+)...........

x+1.......|..........(-)........||....(+)..................(+)..........

Ineq....|...........(+)......||.....(-)..........o......(+)..........

[tex]x \in ]-\infty ; -1 [ U [ -1/4 ; +\infty [[/tex]