$\overline{(\bar{X} + Z\bar{Y} + Y\bar{Z})(\bar{X}+Y\bar{Z})}$
The farthest I've gotten is DeMorgans:
$X(\bar{Z} + Y)(\bar{Y} + Z) + X(\bar{Y} + Z)$
The answer should be $X\bar{Y} + XZ$, but I'm unable to get anywhere close to it. I tried foiling the binomial but it results in a single X value when the whole expression is evaluated, and that's not correct.
Continuing from where you stopped using $1$ for $True$
\begin{eqnarray*} X(\bar{Z} + Y)(\bar{Y} + Z) + X(\bar{Y} + Z) & = & X(\bar{Y} + Z)((\bar{Z} + Y) + 1) \\ & \stackrel{x+1=1}{=} & X(\bar{Y} + Z)\\ & = & X\bar{Y} + XZ \end{eqnarray*}