can a small business owner claim his necessary rental vehicle and to what extent.

If your question is whether the owner of a proprietorship can deduct the expenses for operation of a vehicle used in the business, the answer is "yes." The deduction can be claimed either on a per-mile basis, or actual expenses. The deductible expenses include all ordinary and necessary expenses of the vehicle. If the vehicle is used partly for person purposes, then a ratable share of the expenses can be deducted.