Answer:
[tex]{e}^{x} - x {e}^{ - x} = {e}^{x} (1 - x {e}^{ - 2x} )[/tex]
Step-by-step explanation:
Assuming the given expresion is
[tex] {e}^{x} - x {e}^{ - x} [/tex]
This expression is the same as
[tex] 1 \cdot{e}^{x} - x {e}^{ x} \cdot \: {e}^{ - 2x} [/tex]
We can now factor
[tex] {e}^{x} [/tex]
to get
[tex] {e}^{x} (1 - x {e}^{ - 2x} )[/tex]
Therefore
[tex] {e}^{x} - x {e}^{ - x} = {e}^{x} (1 - x {e}^{ - 2x} )[/tex]
