calculus - L'Hospital's Rule for a fraction where the numerator clearly grows faster than the denominator

According to L'Hospital's Rule, the limit as x approaches infinity of $\frac{8x+5}{6x}$ is simply the derivative of the numerator over the derivative of the denominator is simply $8/6$.

I don't understand why it is $8/6$. $8x+5$ clearly grows faster than $6x$, so shouldn't the limit be infinity?