Complex sentence: Most chemotherapy medications work by destroying fast-growing and/or fast-replicating cancer cells either by causing DNA damage upon replication or other mechanisms; these drugs also damage fast-growing normal cells where they cause serious side effects.
Split into simpler sentences: Most chemotherapy medications work by destroying fast-growing and/or fast-replicating cancer cells, either by causing DNA damage upon replication or by other mechanisms. However, the medications also damage fast-growing normal cells, which may cause serious side effects.