What step am I missing when reducing this boolean function/logic?

Question

I'm trying to reduce a Boolean logic expression. I'm putting the following expression in the Wolfram tool, and visually I understand the answer. I'm missing a step in the reduction, however. What am I missing?

My expression:

C(G~HX+HX+X)

The "answer":

CX

And here's what I reduce it to:

CX(G~H+H)
CX(G+H)
CXG+CXH

What's the step I'm missing that cancels/converts "G+H" to 1 to give me the correct answer?

Answer 1

You factored X (correct operation) but forgot 1: $$ C(G \overline{H} X+HX+X) = C(G \overline{H} +H+1)X = CX.$$

Answer 2

$$\begin{align} C(G \overline{H} X+HX+X) & = CG \overline{H} X+CHX+CX\\ & = (CX)G \overline{H}+(CX)H+(CX)\\ & = CX \end{align}$$