Complex sentence: Van Buren's candidacy split the Democratic vote in New York, throwing that state to the Whigs; at the same time, however, the Free Soilers probably cost the Whigs several Midwestern states.
Split into simpler sentences: Van Buren's candidacy split the Democratic vote in New York, throwing that state to the Whigs. However, at the same time the Free Soilers probably cost the Whigs several Midwestern states.