I’m happy or so I tell myself
New day, more fun!
Okay, so, rational expressions. A polynomial divided by a polynomial.
(if anyone actually finds this, it’s just to help myself understand. May the force be with you if you actually tried to follow any of the directions [I get things wrong, um, occasionally....])
To solve equations with these, multiply numerator by every other denominator. Cancel stuff. Solve normally. THEIR FRACTIONNESS MUST BE GONE FROM THE KINGDOM OF ALGEBRA. It gets rid of the bottoms making them so much freaking easier. oR at least reg hard. (if feel like there’s a sex joke in there somewhere)
To add, find the least common denominator. Basically make the bottoms the same so you can add (which will also change the tops cause symmetry). That involves multiplication, so make sure both the top and bottom are done (not just the bottom Alex stop making the same goddamn mistake lol). Then add. Not multiply something. Not some weird “lets combine EVERYTHING” crap. Adddddddddddddddd. From 3x+1 + -4x-8 to -x-7. Then simplify if possible, which means factor top, factor bottom and cancel LIKE factors. x+5 and x+5, not x+5 and x-5.
Subtracting these just means changing it to an addition problem (just change the minus sign to a plus and then switch the numerator of the second problem’s sign [+4/7 to -4/7 or - to +])
For multiplying,
1. factor
2. Multiple together (a/b) (c/d) = (ac/bd)
3. But cancel the expressions, don’t unfactor!!!!!!! (is that a word? it should be cause I keep making the same mistake)
Division is just flipping the second rational expression and multiplying.
Okay, just one more set of problems until new info, finally.
