Let $\left(x\_n\right)\_{n\in\mathbb{N}\_1},\,x\_n:=\dfrac{a^n+b^n}{a^{n+1}+b^{n+1}}$, where $a,\,b\in\mathbb{R}:a\neq-b$. Then
$$
\lim\_{n\to\infty}\left(\dfrac{a^n+b^n}{a^{n+1}+b^{n+1}}\right)
$$
is...?