The best way to fix a two to three inch shallow rut in your yard is to first loosen the dirt around and under the rut with a garden fork. The idea is to bring the dirt up to the sides of the rut, then spread a little compost over it. Once your compost is in place, then spread your dirt back onto and over the compost. Make sure the top layer is a few inches over the natural ground level to allow for natural settling of the dirt. You can reseed the area or purchase a grass square to place over it. Keep the traffic off of it for a while. Be sure to water regularly.
If the rut is deeper break up the hard ground first and bring up to the soil to the sides of the "bowl" type hole and then fill with one part each of sand, compost and soil. Be sure to rake in the soil that you brought up to the sides of the "bowl" over the fill. You want to add enough soil so that the level is a little higher than the rest of the yard allowing for natural settling of the soil. If your hole is deep, you most likely did not have grass to place on top. Purchase strips or squares of grass for the area so that the soil will stay in the hole. As noted above keep traffic off the area and be sure to water.
If you are selling your home your front yard must say "If you love the yard appeal, wait until you see inside!" It is vitally important to make that yard pop just like that front door!
If you or someone you know wants to sell or buy a home, who would appreciate my level of expertise and service; please call me with their name and phone number I will be happy to follow up with them for you.