"concentrating on both" is correct and can be used in written English.
For example, you could write: We are concentrating on both our short- and long-term goals.
Dozens of collegians who thrive as both pitchers and hitters are forced to choose one or the other as professionals, the theory being that they can't possibly concentrate on both.
I guess my fear when I started at the Hairpin is that I wanted to freelance, but writing every day made me worry that I wasn't going to be able to concentrate on both.
"I cannot concentrate on both.
Future research should concentrate on both the thorough validation of established instruments and the development of new ones.
I wouldn't be able to concentrate on both jobs at once".
I used to run along the line that is painted on a track and I would concentrate on both feet hitting that line".
True, audience members could position themselves to watch both stages at the same time, but the left-right/foreground-background contrast was such that nobody could concentrate on both consistently.
"I'm a person who cares about the present and the future," she said, adding that the first exhibition will concentrate on both the heroic skyscrapers of the 1920's and the new stars now rising in Asia.
At the Brooklyn Academy's Howard Gilman Opera House, Mr. Morris has an English translation of the words projected above the stage; the drawback is that it's occasionally impossible to concentrate on both words and dance, which are many yards apart.
