Réponse :

Explications étape par étape

F = ( x² + 2x - 6 ) - ( x² - 2x - 2 )

⇔ x² + 2x - 6 - x² + 2x + 2

⇔ 4x - 4

E = ( - 2x + 1 ) ( x - 1 ) + 4x² - 1

⇔ E = - 2x² + 2x + x - 1 + 4x² - 1

⇔ E = 2x² + 3x - 2

G = ( x³ - 4x ) + ( x² - 4 )

x³ - 4x + x² - 4 G = x³ - 4x + x² - 4

⇔ G = x³ + x² - 4x - 4

2/ F = 4x - 4

    G = x³ - 4x + x² - 4

⇔ G =  x ( x² - 4 ) + ( x - 2 ) ( x + 2 )

⇔ G = x ( x - 2 ) ( x + 2 ) + ( x - 2 ) ( x + 2 )

3/  R =  ( 8x + 16 ) ( x - 2 ) ( x - 1 )  /  ( x² - 4 ) ( x + 1 )

Condition d'existence:

x² - 4 = 0

( x - 2 ) ( x + 2 )  = 0

x = 2

x = -2

et x + 1 = 0

 ⇔ x = -1

D = R - { -2 , -1 , 2 }

b/  R = 8 ( x + 2 ) ( x - 2 ) ( x - 1 )  /  ( x - 2 ) ( x + 2 ) ( x + 1 )

⇔  R = 8 ( x - 1 )  /  ( x + 1 )

⇔  R = 8x - 8 / ( x + 1 )