Prove that , for every $c \in R$, there exists ${a_{n}}$ of rationals and ${b_{n}}$ of irrationals such that $\lim a_{n} = \lim b_{n} = c$.

Question

Prove that , for every real number $c$, there exists a sequence ${a_{n}}$ of rational numbers and a sequence ${b_{n}}$ of irrational numbers such that $\lim a_{n} = \lim b_{n} = c$, could anyone give me a hint please?

My attempt: one part is answered here For every real number $a$ there exists a sequence $r_n$ of rational numbers such that $r_n$ approaches $a$.