Bonjour,
J'ai un exercice de simplification d'expressions exponentielles à faire. Voici les expressions  et mes réponses :

a) (e^x -1)(2e^-x + 3) = (e^x -1) (2* (1/e^x) + 3)
                                          = (e^x -1) (2/e^x + 3)
                                          ...
                                          = (-e^x + 3e^2x -2) /e^x

b) (1- e^-x)² = 1² - 2 * 1 * e^-x + (e^-x)²
                                                = 1 - 2e^-x + e^-2x
                                                ...
                                                = 1- 2/e^x + 1/e^2x

c) (x-e^x)(x+e^-x) = (x-e^x)(x+ 1/e^x)
                                   ...
                                   = (x²e^x - xe^2x + x - e^x) / e^x

d) (3x + 1/ex)(4+ex) = (12xex + 4 + 3xe2x + ex) / ex

e) (e^-2x)³ * (1-e^6x) = e^-6x * (1-e^6x)
                                                                  ...
                                                                  = (1-e^6x)/ e^6x

f) (2e^x - e^-1)² = (2e^x - 1/e)²
                              = (2e^x)² - 2*2e^x * 1/e + (1/e)²
                              ...
                              = 4e^2x - 4e^x-1 + 1/e²

Est-ce correct ?

Merci d'avance !