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 )