Réponse :
Explications étape par étape
Bonsoir
Ecrire sous la forme d'une fraction la plus simple possible:
a) (3 sur x+8) +5
= 3/(x + 8) + 5
= 3/(x + 8) + 5(x + 8)/(x + 8)
= (3 + 5x + 40)/(x + 8)
= (5x + 43)/(x + 8)
b) (x sur x+1) -3
= x/(x + 1) - 3(x + 1)/(x + 1)
= (x - 3x - 3)/(x + 1)
= (-2x - 3)/(x + 1)
c) 5-(2 sur x^2+1)
= (5(x^2 + 1) - 2)/(x^2 + 1)
= (5x^2 + 5 - 2)/(x^2 + 1)
= (5x^2 + 3)/(x^2 + 1)
d) ( 4x+1 sur x-4) -(3 sur 2)
= (4x + 1)/(x - 4) - 3/2
= [2(4x + 1) - 3(x - 4)] / [2(x - 4)]
= (8x + 2 - 3x + 12) / (2x - 8)
= (5x + 14)/(2x - 8)
Ecrire sous la forme d'une fraction la plus simple possible:
a) (3x sur x+1) -x
= 3x/(x + 1) - x(x + 1)/(x + 1)
= (3x - x^2 - x)/(x + 1)
= (-x^2 + 2x)/(x + 1)
b) (x sur x-2) +4x+2
= x/(x - 2) + (4x + 2)(x - 2)/(x - 2)
= (x + 4x^2 - 8x + 2x - 4)/(x - 2)
= (4x^2 - 5x - 4)/(x - 2)
c) (x(x+1) sur x^2+2) -3
= x(x + 1)/(x^2 + 2) - 3(x^2 + 2)/(x^2 + 2)
= (x^2 + x - 3x^2 - 6)/(x^2 + 2)
= (-2x^2 + x - 6)/(x^2 + 2)
d) (2 sur x-4) +(3 sur x)
= 2/(x - 4) + 3/x
= 2x/[x(x - 4)] + 3(x - 4)/x(x - 4)
= (2x + 3x - 12)/[x(x - 4)
= (5x - 12)/[x(x - 4)]
