You might consider writing an essay in which you compare Hamlet's relationships with Claudius and with Laertes. There are some definite similarities. For instance, Hamlet's relationships both of them were troubled from the beginning of the drama and then deteriorated further, ending in death for all three.
In the beginning of the play, Hamlet and Laertes are known to each other, but they are not friends. Laertes has no respect for Hamlet; he warns Ophelia about Hamlet, believing that Hamlet is dishonest and predatory in his feelings for Ophelia. His distrust and distaste for Hamlet become outright hatred after Polonius is killed. Hamlet's feelings about Laertes become very hostile, also, after the death of Ophelia. Eventually, of course, Laertes is drawn into Claudius' plot to kill Hamlet.
Hamlet's relationship with Claudius is certainly troubled from the beginning as Hamlet and Claudius regard each other with such deep suspicion. Hamlet detests Claudius for marrying Gertrude, and suspects that Claudius had killed Old Hamlet for the throne. Claudius initially attempts to befriend Hamlet, but only because he fears him. As events develop in the play, they become deadly enemies, each secretly plotting against the other.
Hamlet's relationships with Claudius and with Laertes are similar in those respects. From the beginning, both relationships are characterized by deceit. Mutual suspicions then evolve into hatred and lead to destruction.