Rational inequalities

Todo and notes
- while using the safari books online account, I wanted to refresh some high school math (or pre university math). Reading one book about pre calculus (I will likely list it in my goodreads list, see the active sites page) I started to work slowly on the examples before seeing how they were done. Now for the rational inequalities the book claims that the denominator cannot be simplified (without explaining why. Always the same trick, when it gets interesting they leave the exercise to the student, especially the one that can ask no one. Thanks!).
- Well, the method without simplifying the denominator in a rational inequality is surely working and easy to justify (at least in an informal way). I think it is also a preferable way when the denominator is a bit complicated to work out (not only a binomial, but many of them or a complicated formula).
- nonetheless for "simple" denominators one can simplify the denominator keeping in mind its sign. I did some test on paper and I am going to collect the information in pictures but when possible I should move on text. This because text is easier to store over time and moreover the pictures are stored on another service (imgur) that can decide tomorrow to wipe them (although since years it works wonders).

Pictures, see:
- https://i.imgur.com/w4X7sHu.png
- https://i.imgur.com/5Tx92Ah.jpg
- https://i.imgur.com/i8k7xZs.jpg
- https://i.imgur.com/xDshlsT.jpg

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