bonjour
A (x) = ( x - 1 ) ( x - 3 )
A ( x ) + 1 = ( x² - 3 x - x + 3 ) + 1 = x² - 4 x + 4 = ( x - 2 )²
A (x) = - 1
x² - 3 x - x + 3 = - 1
x² - 4 x + 3 = - 1
x² - 4 x + 3 + 1 = 0
x² - 4 x + 4 = 0
( x - 2 )² = 0
x = 2
B (x) / A (x)
( 2 x + 3 )² - ( x + 4 )² / ( x - 1 ) ( x - 3 )
déf sur R \ 1 et 3
S ( x) = ( 2 x + 3 + x + 4 ) ( 2 x + 3 - x - 4 ) / ( x - 1 ) ( x - 3 )
s (x) = ( 3 x + 7 ) ( x - 1 ) / ( x - 1 ) ( x - 3 )
S (x) = 3 x + 7 / x - 3
S (x) = 0
( 3 x + 7 ) / ( x - 3 ) = 0
s'annule en - 7/3 , 3 est valeur interdite
( 3 x + 7 ) / ( x - 3 ) = - 5
( 3 x + 7 ) / ( x - 3 ) + 5 ( x - 3 ) / x - 3 ) = 0
( 3 x + 7 + 5 x - 15 ) / ( x - 3 ) = 0
( 8 x - 8 ) / ( x - 3 ) = 0
S = ( 1 )
