Need suggestion on hardwood refinishing

I am buying a townhouse (closing next month). I am planning to refinish the hardwood floor on the first level (Living rm/Dining rm/ Kitchen/Hallway/Closet/Half bath). The floor is red oak and stained. I am leaning toward natural finish after sanding. Now I have a little problem. In the kitchen, the range and refrigerator sit on hardwood floor. Should I move these two out and sand/finish the two areas under, then move them back and do the rest? Or should I forget about these two areas (but worried about the color difference in the narrow spaces between the appliances and wall/cabinet that people can see)? DIY gurus, any suggestions? Thanks in advance.
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do the entire floor, because you won't ever get it to the same shade if you want to do it later.
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Easy enough to move them out and do the job right. It does not have to be perfect in the rear, but you certainly want the visible part done correctly.
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Make sure it is solid hardwood and not just an engineered wood that cannot be refinished.

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