In Déjà Vu X3 you can show the Preview Pane, hide it, or set it to hide automatically.

Show the Preview Pane

Select the View section of the Ribbon, then click on the downward pointing arrow on the Preview button. In the sub-menu that pops down, click on Normal:

This will set the Preview Pane to be permanently visible in its current position:

Hide the Preview Pane

Select the View section of the Ribbon, then click on the downward pointing arrow on the Preview button. In the sub-menu that pops down, click on Off:

This will set the Preview Pane to be permanently invisible:

Set the Preview Pane to auto-hide

Select the View section of the Ribbon, then click on the downward pointing arrow on the Preview button. In the sub-menu that pops down, click on Auto Hide:

This will set the Preview Pane to be invisible, but a small placeholder for it will be displayed instead:

If you hover the mouse cursor over the placeholder, the Preview Pane will be displayed, over other elements of the Déjà Vu X3 window: