Réponse :
bonjour,
1/x = 5
1/x × x = 5 ×x
1/5 = 5x/5
x = 1/5
3x + 5/- 6x- 4 = - 5x -3/ - 18x - 12
(3x + 5)/( -6x - 4 ) = (- 5x -3)/( - 18x - 12)
on met au même dénominateur
3×(3x + 5)/3×( -6x - 4 ) = (- 5x -3)/( - 18x - 12)
(9x + 15 / -18x -12) - (- 5x -3)/( - 18x - 12) = 0
(9x + 15 ) -( -5x -3 ) / -18x -12 = 0
9x +15 +5x + 3 /-18x -12 = 0
on réduit :
14x +18 / -18x -12 = 0
14x +18 / -6( 3x + 2 ) = 0
-6( 3x + 2 ) × (14x +18 / -6( 3x + 2 )) = 0 ×-6( 3x + 2 )
on simplifie par -6( 3x + 2 )
14x + 18 = 0
14x = -18
x = -18/14
x = -9/7
(2x -7) (6x -4) = (2x -7) (4x +4)
(2x -7) (6x -4) - (2x -7) (4x +4) = 0
on factorise :
(2x - 7 ) ( (6x -4) - (4x +4) ) = 0
on réduit
(2x - 7 ) ( 6x -4 - 4x -4 ) = 0
(2x - 7 ) ( 2x -8 ) = 0
2x - 7 = 0 ou 2x - 8 = 0
2x = 7 2x = 8
x = 7/2 x = 8/2 = 4
voila:)
