When calculating the cost basis for stock, can you use both the commission to purchase the stock and the commission to sell the stock?

You can use each separate commission for each transaction -- in determining the cost basis, and then in computing the sales price. 

For example:

The tax basis of stock you purchase is what you pay for it, plus the commission you pay. Say you buy 100 shares of XYZ Inc. at $40 a share, and you pay a $100 commission. The total cost is $4,100 and the tax basis of each of your shares is $41.

If you sell the 100 shares for same $40 each, and pay $100 commission on the sale, you have a $200 loss—your $4,100 basis minus the $3,900 proceeds of the sale.

Thanks for the great explanation.

your broker does all this arithmetic for you on your 1099-B. There is nothing for you to do but copy the numbers.