Why doesn't Sasuke use his Sharingan to learn Naruto's Rasengan? In the hospital rooftop fight between Sasuke and Naruto, why didn't Sasuke use his Sharingan to learn Naruto's Rasengan? Is it because the Rasengan doesn't use any hand signs? (But Sasuke learns Rock Lee's moves with the Sharingan even if it doesn't rely on hand signs).
Sasuke's chakra affinity is Fire and Lightning.

In the anime, it is speculated by Kakashi that the best chakra affinity to combine the Rasengan with is Wind.

With this in mind, it was probably best for Sasuke to focus primarily on electric or fire based attacks, such as Chidori/Raikiri and Katon. He would be able to elevate these jutsus far more than he can with Rasengan.