Question 13Assume that $x$ is a positive number such that $x-\dfrac1x=3$ and $$\frac{x^{10}+x^8+x^2+1}{x^{10}+x^6+x^4+1}=\frac mn,$$ where $m$ and $n$ are positive integers without common factors larger than $1$. Determine the value of $m+n$.