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Annemarie26
@Annemarie26
May 2019
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Aider moi svp et merci d'avance :
Soit x et y deux nombres réels tels que (x+1) (y-1) + 1 ∉ 0
On pose : a = x+2 / xy-x+y
b = (x+1)y / xy-x+y
Montrer que : (x+1) (a-b +1) =a + b-1
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scoladan
Verified answer
Bonjour,
a + b - 1 = [(x + 2) + (x + 1)y - (xy - x + y)]/(xy - x + y)
= (2x + 2)/(xy - x + y) = 2(x + 1)/(xy - x + y)
a - b + 1 = [(x + 2) - (x + 1)y + (xy - x + y)]/(xy - x + y)
= 2/(xy - x + y)
⇒ (x + 1)(a - b + 1) = 2(x + 1)/(xy - x + y) = a + b - 1
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Thanks 1
Annemarie26
merci beaucoup pour votre aide
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Lista de comentários
Verified answer
Bonjour,a + b - 1 = [(x + 2) + (x + 1)y - (xy - x + y)]/(xy - x + y)
= (2x + 2)/(xy - x + y) = 2(x + 1)/(xy - x + y)
a - b + 1 = [(x + 2) - (x + 1)y + (xy - x + y)]/(xy - x + y)
= 2/(xy - x + y)
⇒ (x + 1)(a - b + 1) = 2(x + 1)/(xy - x + y) = a + b - 1