Another Question On Using Basics Limit Arithmetics Given $\lim \limits_{n\to \infty}\frac{a_n}{b_n}=1$  
is this claim $\lim \limits_{n\to \infty}(a_n-b_n)=0$ false or true?
I think it's false because I can't talk about $\lim \limits_{n\to \infty}a_n$ nor about $\lim \limits_{n\to \infty}b_n$ however, I can't find an example that will disprove the claim.
Thank you.

Hint: try a quotient of polynomials of the same degree.
