When renting out part of your personal residence, can you depreciate a % of the common rooms?

SURE!    But if something sounds to good to be true, it usually is. When you sell your home, the Home Sale Exclusion does not apply to the part of the home that you have depreciated.  And, to further beat a man when he is down, the part of the sale price that you allocate (in the same proportion), to the depreciated area, is subject to the depreciation recapture at ordinary income tax rate and the part of the sale (in same proportion) that is greater than your original cost for that part of the home, is subject to taxation also,,at capital gain rate hopefully.

If you receive rental income for the use of a dwelling unit, such as a house or an apartment, you may deduct certain expenses. These expenses, which may include mortgage interest, real estate taxes, casualty losses, maintenance, utilities, insurance, and depreciation, will reduce the amount of rental income that's subject to tax. You'll generally report such income and expenses on Form 1040, U.S. Individual Income Tax Return or Form 1040-SR, U.S. Tax Return for Seniors and on Schedule E (Form 1040), Supplemental Income and Loss. 

If you use the dwelling unit for both rental and personal purposes, there are certain limitations, including you can't deduct a loss.

@ehammondcpa  is correct for Schedule C and other "Earned Income' situations, but you could do what you are asking.  I just don't know why you would based on events that most likely will happen in the future.