bonjour;

a+b/a-b

= 5/6 +(9/20)/(5/6) - 9/20

= 5/6 +9/20*6/5 +9/20

= 5/6 + 54/100+9/20

=  500/600 +324/600 + 270/600

= 1 094/600

= 547/300

ab-b/ab

(5/6 * 9/20) - (9/20) / (5/6*9/20)

= 5/6 *20/9 - (9/20) / (5/6*20/9)

= 100/54 -(9/20)/(100/54)

= 100/54 -9/20 *54/100

= 100/54 -486/2 000

= 50/27 - 243/ 1 000

= 50/27* 1 000/ 1000  - 243/1000* 27/27

= 50 000/27 000- 6 561/27 000

= 43 479/ 27 000

= 14 493/ 9 000

= 4 831/ 3 000

Verified answer

Explications étape par étape:

(a+b)/(a-b) = (5/6 + 9/20) / (5/6 - 9/20) =

(50/60 + 27/60) / (50/60 - 27/60) =

( 77/60 ) / (23/60) =

77/60 × 60/23 = 77/23

ab-b /ab =[ (5/6 × 9/20) - 9/20] / (5/6 × 9/20) =

[ (5/2×3/20) - 9/20] / (5/2 × 3/20) =

( 15/60 - 27/60) / 15/60 =

-12/60 / 15/60 = -12/60 × 60/15 =

-12/15 = -4/3