STEP-BY-STEP ANSWER:
Step 1: Recognize that alkylating agents add alkyl groups to the DNA of rapidly dividing cells.
Step 2: Explain that this alkylation results in cross-linking of DNA strands, ultimately preventing DNA replication and cell division.
Step 3: Note that the mechanism makes these agents effective in targeting cancer cells, which divide rapidly.
Step 4: Discuss their role in immunosuppression where they reduce the activity of the immune system, beneficial in conditions like organ transplantation.
Final Answer: Alkylating agents work by damaging the DNA of rapidly dividing cells, making them effective in cancer treatments and in immunosuppressive therapy.