équations

[lucasse27]

voila je viens juste de terminer mes exo mais je voudrai appronfondir;;;
1) 1/x + 1/x+2 = 0 2) 3/x-2 - 1/x+1 = x+4/(x+1)(x-2)

3)2x-1/x = 2x+1/x+2 4) 1/x+1 - 2/x-1 = x-5/x2 -1

merci de votre aide

[yvelines78]

bonjour,

1/x+1/x+2=0
(x+2)+x/x(x+2)=0
donc (x+2)+x=0
2x+2=0
x=-1

3/x-2 -1/x+1 = x+4/(x+1)(x-2)
3(x+1)-(x-2) /(x-2)(x+1) = x+4 /(x+1)(x-2)
3(x+1)-(x-2)=x+4
3x+3-x+2=x+4
2x+5=x+4
2x-x=4-5
x=-1

2x-1/x=2x+1/x+2
(2x-1)(x+2)=x(2x+1)
2x²-x+4x-2=2x²+x
3x-2=x
3x-x=2
2x=2
x=1

1/x+1 -2/x-1 =x-1/x²-1
(x-1)-2(x+1) /(x+1)(x-1) =x-1/x²-1
x-1-2x-2/x²-1=x-1/x²-1
-x-3=x-1
-3+1=x+x
-2=2x
x=-1