How to work out these fractions?

Question

$\dfrac{-x^4 + 4x^2 + 6}{x}$

$\dfrac{7x^8 - 5x^5 + 9x^3 + x^2}{x}$

I have no idea how to do this. I was first thinking of doing $-x$ or collecting up the $x's$ but I'm not sure as I haven't dealt with these before. Thanks.

Answer 1

You can divide term by term. The first will leave you with a $\frac 6x$ at the end, so may not be seen as simpler. As there is a factor $x$ in every term of the numerator, it will eliminate the fraction. In some applications, you need to keep track of the fact that $x$ cannot be zero, even after you clear the fraction. In others, you can allow it as a limit.