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Effectuer des simplifications sous la forme ef(x)f est une fonction affine    ressource 4401

Soit x un nombre réel. Associez chaque calcul au résultat correspondant.

e - 65 x - 91 e - 45 x - 63 e - 25 x - 35 e 15 x + 21
e - 5 x - 7  ×  e - 20 x - 28 TemplateBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", RowBox[List[RowBox[List["5"]], " ", "x"]]]], "-", "7"]]], "\"\[ThinSpace]\[Times]\[ThinSpace]\"", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", RowBox[List[RowBox[List["20"]], " ", "x"]]]], "-", "28"]]]], "Row", Rule[DisplayFunction, Function[RowBox[List[Slot[1], "\[InvisibleSpace]", Slot[2], "\[InvisibleSpace]", Slot[3]]]]], Rule[InterpretationFunction, Function[RowBox[List["Row", "[", RowBox[List["{", RowBox[List[Slot[1], ",", Slot[2], ",", Slot[3]]], "}"]], "]"]]]]] =
e - 7 - 5 x e - 28 - 20 x TagBox[FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "7"]], "-", RowBox[List["5", " ", "x"]]]]], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "28"]], "-", RowBox[List["20", " ", "x"]]]]]], HoldForm] =
e - 7 - 5 x  ×  e - 28 - 20 x e 56 + 40 x TagBox[FractionBox[TemplateBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "7"]], "-", RowBox[List["5", " ", "x"]]]]], "\"\[ThinSpace]\[Times]\[ThinSpace]\"", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "28"]], "-", RowBox[List["20", " ", "x"]]]]]], "Row", Rule[DisplayFunction, Function[RowBox[List[Slot[1], "\[InvisibleSpace]", Slot[2], "\[InvisibleSpace]", Slot[3]]]]], Rule[InterpretationFunction, Function[RowBox[List["Row", "[", RowBox[List["{", RowBox[List[Slot[1], ",", Slot[2], ",", Slot[3]]], "}"]], "]"]]]]], SuperscriptBox["\[ExponentialE]", RowBox[List["56", "+", RowBox[List["40", " ", "x"]]]]]], HoldForm] =
e - 7 - 5 x e - 28 - 20 x  ×  e 56 + 40 x TagBox[FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "7"]], "-", RowBox[List["5", " ", "x"]]]]], TemplateBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "28"]], "-", RowBox[List["20", " ", "x"]]]]], "\"\[ThinSpace]\[Times]\[ThinSpace]\"", SuperscriptBox["\[ExponentialE]", RowBox[List["56", "+", RowBox[List["40", " ", "x"]]]]]], "Row", Rule[DisplayFunction, Function[RowBox[List[Slot[1], "\[InvisibleSpace]", Slot[2], "\[InvisibleSpace]", Slot[3]]]]], Rule[InterpretationFunction, Function[RowBox[List["Row", "[", RowBox[List["{", RowBox[List[Slot[1], ",", Slot[2], ",", Slot[3]]], "}"]], "]"]]]]]], HoldForm] =
( e - 7 - 5 x TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "7"]], "-", RowBox[List["5", " ", "x"]]]]], HoldForm] ) 5 TagBox["5", HoldForm] =
( e - 7 - 5 x ) 5  ×  e - 20 x - 28 TemplateBox[List[SuperscriptBox[RowBox[List["(", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "7"]], "-", RowBox[List["5", " ", "x"]]]]], HoldForm], ")"]], TagBox["5", HoldForm]], "\"\[ThinSpace]\[Times]\[ThinSpace]\"", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", RowBox[List[RowBox[List["20"]], " ", "x"]]]], "-", "28"]]]], "Row", Rule[DisplayFunction, Function[RowBox[List[Slot[1], "\[InvisibleSpace]", Slot[2], "\[InvisibleSpace]", Slot[3]]]]], Rule[InterpretationFunction, Function[RowBox[List["Row", "[", RowBox[List["{", RowBox[List[Slot[1], ",", Slot[2], ",", Slot[3]]], "}"]], "]"]]]]] =