I want to estimate with big O the following expressions:$$\begin{align*}f_1(x) &= \frac{x^4 + x^2 + 1}{x^4 + 1}, \\f_2(x) &= \frac{x^3 + 5 \log x}{x^4 + 1}.\end{align*}$$How do you eliminate the constant on the bottom of the fraction? How would you work to solve these types of problems?
How to solve this big O notation of a fraction
asymptotics