Bonjour tout le monde,pouvez vous m'aidez à faire les exercices 38 et 39 merci d'avance

Bonsoir

38)
r + s - t

a. r = 1/2 ; s = 3/4 ; t = 1/4
1/2 + 3/4 - 1/4
= 1 x 2 / 2 x 2 + 3/4 - 1/4
= 2/4 + 3/4 - 1/4
= 4/4
= 1

b. r = 7/6 ; s = 10/3 ; t = 5/6
7/6 + 10/3 - 5/6
= 7/6 + 10 x 2 / 3 x 2 - 5/6
= 7/6 + 20/6 - 5/6
= 22/6
= 2 x 11 / 2 x 3
= 11/3

c. r = 1/3 ; s = 1/9 ; t = 1/27
1/3 + 1/9 - 1/27
= 1 x 9 / 3 x 9 + 1 x 3 / 9 x 3 - 1/27
= 9/27 + 3/27 - 1/27
= 11/27

d. r = 2/5 ; s = 13/15 ; t = 2/5
2/5 + 13/15 - 2/5
= 2 x 3 / 5 x 3 + 13/15 - 2 x 3 / 5 x 3
= 6/15 + 13/15 - 6/15
= 13/15

e. r = 13/18 ; s = 19/6 ; t = 4/3
13/18 + 19/6 - 4/3
= 13/18 + 19 x 3 / 6 x 3 - 4 x 6 / 3 x 6
= 13/18 + 57/18 - 24/18
= 46/18
= 2 x 23 / 2 x 9
= 23/9

39)
a. 1/2 + 1/4 = 1 x 2 / 2 x 2 + 1/4 = 2/4 + 1/4 = 3/4

b. 1/2 + 1/4 + 1/8 = 1 x 4 / 2 x 4 + 1 x 2 / 4 x 2 + 1/8 = 4/8 + 2/8 + 1/8 = 7/8

c. 1/2 + 1/4 + 1/8 + 1/16
= 1 x 8 / 2 x 8 + 1 x 4 / 4 x 4 + 1 x 2 / 8 x 2 + 1/16
= 8/16 + 4/16 + 2/16 + 1/16
= 15/16

d. 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64
= 1 x 32 / 2 x 32 + 1 x 16 / 4 x 16 + 1 x 8 / 8 x 8 + 1 x 4 / 16 x 4 + 1 x 2 / 32 x 2 + 1/64
= 32/64 + 16/64 + 8/64 + 4/64 + 2/64 + 1/64
= 63/64