Show that any continuous-time signal $x(t)$ can be represented as $x(t)= x_e(t) + x_o(t)$ Show that any continuous-time signal $x(t)$ can be represented as $x(t)= x_e(t) + x_o(t)$

where $x_e(t) =\frac{1}{2}[x(t) + x(-t)]$ and $x_o(t) = \frac{1}{2}
[x(t) − x(-t)]$
are even and odd functions, respectively.
Substitute the last two equations into the first and it should be clear.

iI.e., if you have $x_e(t), x_o(t)$  given to you. Substitute these into the equation for $x(t)$ and you should see that both sides are equal to each other.  

(Note that this proves the equality, but doesn't prove that $x_e(t)$ is even or that $x_o(t)$ is odd.)