8. Recently, an article on the internet has gone viral. It originates from a common question, as shown in Figure 1. This seemingly easy-to-solve problem actually contains profound wisdom.

Let $a, b \in\{2,3, \cdots, 8\}$. Then the maximum value of $\frac{a}{10 b+a}+\frac{b}{10 a+b}$ is $\qquad$
8. $\frac{89}{287}$.

Assume $a \geqslant b, x=\frac{a}{b}$. Then $1 \leqslant x \leqslant 4$,

and $\square$
$$
\begin{array}{l}
\frac{a}{10 b+a}+\frac{b}{10 a+b}=\frac{x}{10+x}+\frac{1}{10 x+1} \\
=\frac{10 x^{2}+2 x+10}{10 x^{2}+101 x+10} \\
=1-\frac{99 x}{10 x^{2}+101 x+10} \\
=1-\frac{99}{10\left(x+\frac{1}{x}\right)+101} .
\end{array}
$$

When $x=4$, i.e., $\{a, b\}=\{2,8\}$, the above expression reaches its maximum value $\frac{89}{287}$.