# How Can The Following Language Possibly Be Regular?

$$L =$$ {$$(01)^ax(10)^b$$ | $$a=b, b > 0, x∈$${$$0,1$$}*}

This is a question where according to the key, yes, the language is regular, but no explanation is given. However, if $$a=b$$, then this can be rewritten as:

$$L =$$ {$$(01)^nx(10)^n$$ | $$n > 0, x∈$${$$0,1$$}*}

And $$L =$$ {$$(01)^n(10)^n$$ | $$n > 0$$} is a famous example of an expression which is NOT regular, so how on earth could inserting the $$x$$ in between the first two exponents allow it to be regular? I'm just not seeing any regular expression that could describe this, which is necessary for a language to be regular. What am I missing?

Since $$x$$ can be anything, it can swallow most of the 01s and 10s. So it's the same as $$\{01x10:x\in\{0,1\}^*\}$$.
Hint: The intermediate symbol $$x$$ has no impact on the non-regularity of the language. The general method to show that a language is non-regular is the pumping lemma and this language is similar to $$\{a^nb^n\mid n\geq 1\}$$ or better $$\{a^nxb^n\mid n\geq 1\}$$.