If you've got money, the advise really is don't. But if you want to save some cash, allow it to cool down, filter it, then store it. Use it twice or most three times. As much as possible, use it with the same type of food. If it smells rancid and there are so many particles, then don't use it. I do re use my oil, btw.
I remember my mother, grandmother and other family members doing that because we grew up poor. After the third use it would leave a funky taste on the meat but who was I to complain back then. I was lucky to have a pork chop. Now I will reuse oil two times if it doesn't have anything in it or if it still looks and smells clean.
I have heard the same thing about previously used oil being carcinogenic. If I understand it correctly (which I probably don't, lol), heat changes oil's molecular structure, making it unhealthful (carcinogenic). That is why healthfood gurus advise consuming only cold-pressed oil, rather than heat-refined oil. Heat-refined oil, even if it's canola oil or oilive oil, is unhealthy right out of the bottle, even though labels often tout how healthy the oils are. It's also a reason that fried foods are bad for you, in addition to their high fat content. Foods fried in previously heated oils are doubly bad for you. The higher the temperature and the more times oil is heated, the worse the oil is for you.
Read labels and look for the phrase 'cold-pressed.' It can be hard to find! If it doesn't specifically state that it's cold-pressed, it's probably heat refined. When it's heat refined, the manufacturer usually does not point that out.
I reuse oil that was used for vegetables, such as hash browns or tater tots. I learned to do this more than 25 years ago when working part-time at McDonalds during school hours. They drained and strained the oil used for french fries and apple pies, and then put it back in the fryers for another day's use.
However, I never reuse oil that cooked fish or meat. Rather than waste fresh cooking oil on meat, I use what has already been strained a few times from cooking vegetables.
I use about twelve tablespoons of oil a year, most of which I use in the two-month, holiday, baking season; and those twelve tablespoons are consumed with whatever baked goods they were added to. I open a bottle of oil in November, and throw out what's left of it as the following November approaches (and buy a new one for the new holiday season). Most often the expiration date on the label is either close or past, but even if it isn't I don't want to use something that's been open for ten months.
If I did ever use a substantial amount of oil (or if I ever decide to), I couldn't make myself re-use it (unless, maybe, the subsequent use was on the same day and maybe very close to the first "cooking session"; and maybe even a matter of a variety of fried foods that would be served together on the same plate. Carcinogenic or not - to me, using "food contaminated" oil on another day isn't an idea that appeals to me.