Bonjour, je suis en 4ème, pouvez-vous m’aider svp merci et bonne fête de fin d'année.

Bonjour

1.
A = (3 / 5 - 1 / 2) x (5 / 2)
= [ (3 x 2) / (5 x 2) - (1 x 5) / (2 x 5) ] x (5 / 2)
= (6 / 10 - 5 / 10) x (5 / 2)
= [ (6 - 5) / 10 ] x (5 / 2)
= (1 / 10) x (5 / 2)
= (1 x 5) / (10 x 2)
= 5 / (2 x 5 x 2)
= 1 / 4

B = [ 3 - (2 / 3) ] / [ (4 / 3) x 7 ]
=  [ (3 x 3) / (1 x 3) - (2 / 3) ] / [ (4 x 7) / 3 ]
= (9 / 3 - 2 / 3) / (28 / 3)
= [ (9 - 2) / 3 ] / (28 / 3)
= (7 / 3) / (28 / 3)
= (7 / 3) x (3 / 28)
= (7 x 3) / (3 x 28)
= (7 x 3) / (3 x 4 x 7)
= 1 / 4

Donc A = B = 1 / 4

2.
C = (8 / 3) - (2 / 3) / (8 / 7)
= (8 / 3) - (2 / 3) x (7 / 8)
= (8 / 3) - (2 x 7) / (3 x 8)
= (8 / 3) - (2 x 7) / (3 x 2 x 4)
= 8 / 3 - 7 / 12
= (8 x 4) / (3 x 4) - 7 / 12
= 32 / 12 - 7 / 12
= (32 - 7) / 12
= 25 / 12

D = [ -2 / 5 + 5 / 2 ] / [ -3 / 4 + 1 / 2 ]
= [ (-2 x 2) / (5 x 2) + (5 x 5) / (2 x 5) ] / [ -3 / 4 + (1 x 2) / (2 x 2) ]
= (-4 / 10 + 25 / 10) / (-3 / 4 + 2 / 4)
= [ (-4 + 25) / 10) / [ (-3 + 2) / 4 ]
= (21 / 10) / (-1 / 4)
= (21 / 10) x (4 / (-1))
= (21 x 4) / (10 x (-1))
= (21 x 2 x 2) / (2 x 5 x (-1))
= 42 / (-5)
= -42 / 5

3. Inverse de B :
4 / 1 = 4
   
   Opposé de D :
42 / 5

4. B + D
= 1 / 4 + (-42) / 5
= (1 x 5) / (4 x 5) + (-42 x 4) / (5 x 4)
= 5 / 20 + (-168) / 20
= (5 - 168) / 20
= -163 / 20

   C x D
= (25 / 12) x (-42 / 5)
= (25 x (-42)) / (12 x 5)
= (5 x 5 x (-21) x 2) / (6 x 2 x 5)
= -105 / 6
= (-105 / 3) / (6 / 3)
= -35 / 2

Voilà j'espère avoir pu t'aider ^^