Réponse:
bonjour tout d'abord
[tex] {e}^{a} \times {e}^{b} = {e}^{a + b} [/tex]
[tex] {e}^{a} \div {e}^{b} = {e}^{a - b} [/tex]
[tex] a(x) = {e}^{2x + 1 - 4x} = {e}^{ - 2x + 1} [/tex]
[tex]b(x) = {e}^{2x - 1 - (5x - 2)} \times {e}^{ - x} [/tex]
[tex]b(x) = {e}^{ - 3x + 1 - x} = {e}^{ - 4x + 1} [/tex]
[tex]c(x) = {e}^{ - x - 6} \div ({e}^{ - 2x} \times e)[/tex]
[tex]c(x) = {e}^{ - x - 6 + 2x - 1} = {e}^{x - 7} [/tex]
[tex]2) \: \: \: {e}^{ - x} - {e}^{ - 2x} = \frac{1}{ {e}^{x} } - \frac{1}{ {e}^{2x} } [/tex]
[tex] = \frac{ {e}^{2x} }{ {e}^{x} {e}^{2x} } - \frac{ {e}^{x} }{ {e}^{x} {e}^{2x} } [/tex]
[tex] = \frac{ {e}^{x} ( {e}^{x} - 1) }{ {e}^{x} \times {e}^{2x} } [/tex]
[tex] = \frac{ {e}^{x} - 1 }{ {e}^{2x} } [/tex]
