bonjour
résoudre dans R
a) x+2/-4x+1>0
x + 2 = 0 et -4x + 1 # 0
x = -2 et 4x # 1
x = -2 et x # 1/4
x..............|-inf............-2.........1/4.........+inf
x + 2.......|.......(-)........o...(+)..........(+).........
-4x + 1....|........(+)............(+)...o.....(-).........
Ineq........|........(-).......o....(+)...||.....(-)........
[tex]x \in ]-2 ; 1/4[[/tex]
a) 5x-1/-3x>ou égale 0
5x - 1 = 0 et -3x # 0
5x = 1 et x # 0
x = 1/5 et x # 0
x..............|-inf............0.........1/5.........+inf
5x - 1.......|.......(-)............(-).....o....(+).........
-3x...........|........(+).....o...(-)...........(-).........
Ineq........|........(-).......||....(+)...o.....(-)........
[tex]x \in ]0; 1/5][/tex]
c) 7x-3/(-8x-1)²<0
7x - 3 = 0 et (-8x - 1)^2 (carré donc toujours > 0)
7x = 3 et -8x - 1 # 0
x = 3/7 et 8x # -1
x = 3/7 et x # -1/8
x..............|-inf.........-1/8.........3/7.........+inf
7x - 3.......|.......(-)............(-).....o.....(+).........
(-8x - 1)^2|......(+)......o....(+)............(+).........
Ineq........|........(-)......||....(-)......o......(+)........
[tex]x \in ]-\infty ; -1/8[ U ]-1/8 ; 3/7[[/tex]