Réponse :

Explications étape par étape

Bonjour,

Ecrire sous forme d'une seule fraction de la manière la plus simple possible :

a) 1/(x + 1) - 3/x

= x/[x(x + 1)] - 3(x + 1)/[x(x + 1)]

= (x - 3x - 3)/[x(x + 1)]

= (-2x - 3)/[x(x + 1)]

b) (2x + 4)/(x - 2) + 1/2

= 2(2x + 4)/[2(x - 2)] + (x - 2)/[2(x - 2)]

= (4x + 8 + x - 2)/[2(x - 2)]

= (5x + 6)/[2(x - 2)]

c) 4/(x - 4) - 3/(x + 1)

= [4(x + 1) - 3(x - 4)]/[(x + 1)(x - 4)]

= (4x + 4 - 3x + 12)/[(x + 1)(x - 4)]

= (x + 16)/[(x + 1)(x - 4)]

d) (2x + 2)/(2x - 1) + 3x/(x + 3)

= [(2x + 2)(x + 3) + 3x(2x - 1)]/[(2x - 1)(x + 3)]

= (2x² + 6x + 2x + 6 + 6x² - 3x)/[(2x - 1)(x + 3)]

= (8x² + 5x + 6)/[(2x - 1)(x + 3)]