bonsoir
B(x) = x/(x - 1) + 2
1) montrer que B(x) = (3x - 2)/(x - 1) :
B(x) = x/(x - 1) + 2(x - 1)/(x - 1)
B(x) = (x + 2x - 2)/(x - 1)
B(x) = (3x - 2)/(x - 1)
2) Résoudre B(x) = 0 :
x - 1 # 0
x # 1
3x - 2 = 0
3x = 2
x = 2/3
3) A(x) = (x^2 + 2x - 2)/(x - 1)
a) A(11) = (11^2 + 2 * 11 - 2)/(11 - 1) = (121 + 22 - 2)/10 = (121 + 20)/10 = 141/10 = 14,1
B(11) = (3 * 11 - 2)/(11 - 1) = (33 - 2)/10 = 31/10 = 3,1
A(11) - B(11) = 14,1 - 3,1 = 11
b) montrer que A(x) - B(x) = x :
= (x^2 + 2x - 2)/(x - 1) - (3x - 2)/(x - 1)
= (x^2 + 2x - 2 - 3x + 2)/(x - 1)
= (x^2 - x)/(x - 1)
= x(x - 1)/(x - 1)
= x
