You are welcome!
Could be made much easier than describing but I'll try.
select the ax and set stroke join rounded in the fill and stroke tab (Shift+Ctrl+F)
-there are some corners on the graphic that looks off with miter joins-
select the path in the background and edit its nodes
-an ax was already substracted from it so it's not overlapping with the current one, producing gaps;
just select all nodes falling in a vertical line and scale them so they will be hidden behind the ax-
select the ax and convert strokes to path (Ctrl+Alt+C)
break path apart (Ctrl+Shift+K)
deselect the largest path by Shift+click
combine the rest together (Ctrl+K)
select the path in the background and the largest from the ax and add them together (Ctrl++)
select both paths and subtract the top one from the bottom one (Ctrl+-)
In a nutshell.
Usually it helps to track the process better if you set a vivid fill and 50% opacity to the paths so you see where the objects overlap and can see better which path you are selecting.
