Réponse :
Explications étape par étape
Bonjour
A = 2/3 - 2/3 x 9/5
A = 2/3 - 9/3 x 2/5
A = 2/3 - 3 x 2/5
A = 2/3 - 6/5
A = (2 x 5)/(3 x 5) - (6 x 3)/(5 x 3)
A = 10/15 - 18/15
A = (-8)/15
B = (1/6 - 1/3) : (2/5 x 3/4)
B = (1/6 - 2/6) : (2/4 x 3/5)
B = (-1/6) : (1/2 x 3/5)
B = (-1/6) : 3/10
B = (-1/6) x 10/3
B = -10/6 x 1/3
B = -5/3 x 1/3
B = (-5/9)
c) A/B
A/B = (-8/15) : (-5/9)
A/B = -8/15 x -9/5
A/B = 9/15 x 8/5
A/B = (3 x 3)/(3 x 5) x 8/5
A/B = 3/5 x 8/5
A/B = 24/25
3)a) la somme de A et de l’inverse de B :
= A + 1/B
= -8/15 - 9/5
= -8/15 - (9 x 3)/(5 x 3)
= -8/15 - 27/15
= (-35/15)
= (-7 x 5)/(3 x 5)
= (-7/3)
b) le produit de B par l’opposé de A :
= B x (-A)
= (-5/9) x 8/15
= (-5/15) x 8/9
= -5/(3 x 5) x 8/9
= -1/3 x 8/9
= -8/27
