Ok this is gonna be pretty basic... But I just want to make sure I got this reasoning right. This formula:
The last transformation after the multipication/division. This is what's going on, right? (excuse the writing)
Basically it's rearranging the multiplications terms, then separating the fraction in two, and then applying the rule
$$\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b}*\frac{d}{c}$$
backwards to turn the $\frac{x}{ln(x+1)}$ back into $\frac{ln(x+1)}{x}$, right?
Tangential question, if the limit of $\frac{ln(x+1)}{x} = 1$, wouldn't the limit of $\frac{x}{ln(x+1)} = 1^{-1} = 1$? Letting usk "skip" turning it upside down again?