OK, getting rid of scratches on hard wood floors or furniture can work out to be very very expensive.
This is a tried and tested tip to make these scratches almost invisible (it will not remove them completely, that is really a french polishers job).
OIL and VINEGAR. Yup oil and vinegar. If you mix on part vinegar with one part olive oil (or any type of vegetable, sunflower oil, basically an oil you would use to cook with). Mix as well as you can and pour on the area with the scratches. Leave it to soak in for 12-24 hours and then rub off with a dry cloth.
The oil softens the scratches and the vinegar removes any dirt that makes the scratches visible. If it's a clean scratch, just use the oil, the vinegar helps better when and item needs a bit of a clean too. Works a treat on antique furniture that you may want to sell but have the additional costs of geting re-furbished.
Hope this is useful to you.