Why can $\lvert \cfrac{3}{x} - 3 \rvert$ be turned into $\cfrac{3}{\lvert x \rvert} \lvert x-1 \rvert$? Where can I find more rules/tricks like this?
2026-03-25 20:51:23.1774471883
Absolute Value Rules
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You can factor and take the absolute value of the factor out.
That is $$ |xy|=|x||y|$$
You can also switch the signs inside absolute value that is
$$|x-y|=|y-x|$$