Expand this expression to the greatest possible terms with the lowest possible exponents.
$\ln\left[\dfrac{(4x^5-x-1)\sqrt{x-7}}{(x^2+1)^3}\right]$
There are two ways at which I approached this problem...
So for the first one, I started out by giving each set of parenthesis their own $\ln$ function:
$\ln(4x^5-x-1)+\ln(\sqrt{x-7})-\ln(x^2+1)^3$
My second approach was to factor out the bottom and then hopefully divide it by the top...
$\ln\left[\dfrac{(4x^5-x-1)\sqrt{x-7}}{x^6+3x^4+3x^2+1}\right]$
And my next plan was to divide $4x^4-x-1$ by $x^6+3x^4+3x^2+1$
Can someone tell me which approach is the correct way, or if they are both wrong. Please do not give full answers' only hints.