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 )
