Checking my understanding of right quotient So I am trying to fully understand the concept of quotient languages.

I will give some examples, let me know if this is correct:
Say that 

L1={} and L2 is {ot}, then L1/L2 is {carr}
Or if L1=ab*c and L2 is b*c then L1/L2 is a.


If this is it, I will then try to approach more complex concepts :)
Thank you!
If $L_1=ab^*c$ and $L_2$ is $b^*c$ then $L_1/L_2$ is $ab^*$.

Note that the $b$'s are not forced to disappear.
For instance (as part of these languages) $\{ab^{10}c\}/\{b^3c\} = \{ab^7\}$.