Bonjour ;
a.
A = ab + cd = 2/3 x (- 1/4) + 2/5 x (- 1/2)
= - 2/3 x 1/4 - 2/5 x 1/2
= - (2 x 1)/(3 x 4) - (2 x 1)/(5 x 2)
= - 2/12 - 2/10
= - 1/6 - 1/5
= - (1/6 + 1/5)
= - ((5 x 1)/(5 x 6) + (6 x 1)/( 5x 6))
= - (5/30 + 6/30)
= - (5 + 6)/30
= - 11/30 .
b.
On a : a + d = 2/3 - 1/2
= (2 x 2)/(3 x 2) - (1 x 3)/(2 x 3)
= 4/6 - 3/6
= (4 - 3)/6 = 1/6 ;
et : b + c = - 1/4 + 2/5 = - (1 x 5)/(4 x 5) + (2 x 4)/(4 x 5)
= - 5/20 + 8/20
= (- 5 + 8)/20
= 3/20 ;
donc : (a + d)/(b + c) = (1/6)/(3/20) = 1/6 x 20/3
= (1 x 20)/(6 x 3)
= 20/18
= 10/9 .
