(x+a)=\frac{2}{x-a}(x-a)(x+a)](https://s0.wp.com/latex.php?latex=%5Cleft%5B%5Cfrac%7B1%7D%7Bx-a%7D%2B%5Cfrac%7B1%7D%7Bx%2Ba%7D%5Cright%5D%28x-a%29%28x%2Ba%29%3D%5Cfrac%7B2%7D%7Bx-a%7D%28x-a%29%28x%2Ba%29&bg=ffffff&fg=000&s=2&c=20201002)
Original Transcript
All right, kids. I’m going to start this here crash course off here. I’m uh I’m doing a few different um levels of math on Plem Academy for just basic review of how to solve problems quickly and efficiently and then a more in-depth full circle of math problems. So, we’ll start off here with a algebra an algebra problem. Let me just duplicate this here. And so I’m going to do this as the crash course. So the crash course is just going to be me solving problems quickly from different subjects in order so that you guys understand. So I’ll do 1.0 will be algebra, college algebra. We’ll start with um with that. This will be a book that you can purchase at some point. And we’ll start with college algebra. So, I’m just going to I’m going to I’m going to take questions from the algebra book. And under algebra, we’ll start here with we’ll just do it one at a time. This is I’ll I’m just going to take random questions from different situations. So, we’ll start here under um chapter 1 linear functions. This is the Sullivan the Sullivan algebra book which is number 19. So from 19 we’ll do we’ll do equations and inequalities. So let me get the we’ll get the
chapter one equations and inequalities and then linear functions. So we will do it like this 1.1. So I’ll just do I’ll just I’ll do it like this. I’ll label it one and do this divider here and then that divider. And so then this will be
college algebra portion of the book. We’ll make that heading one. This will be heading two. This will be heading three. And then I want
a question. So I’m going to go to the back of the book and also reference that this is book 19. So I’ll put 19. Book 19 right there. That’s book 19 you see right here. And that’s book 19. So under linear equations, let’s take a question here. And we will start with um we’ll just start with something. They want us to solve for I’ll do something pretty basic here. Let’s let’s do solve each equation. The letters A, B, and C are constants. Uh so we want to solve equations. So I’ll do I’ll do number 73 here.
All right. So then how I do this is I do a I type the word question and then I do triple equal sign and then I will type it in here. So solve for x should be in the equation editor and 1 /x – a + 1 over x + a is equal to 2 overx minus a. So I’m I’m just going to be solving these quick the way you would want to solve them on an exam. basically. Okay. And answer. And so for the answer then I do I’m just dividing this out. This is number number 73 from 1.1.
So number 73 from 1.1 and that is 73 says x is equal to a^2
x is equal to a^2. All right so the this particular crash course book that I’m writing is specifically for how you’re going to solve for exam questions. [snorts] I I should this is the first one in the book. So I’m going to do this the way you would want to solve this for an exam question. So exam solution I’ll just actually I’ll do it this way.
This particular book is just for those of you who want to understand how to do this quick and easy. Okay, not the elaborate in-depth. There’s different guys. There’s slaying math, application of math, and then there’s math, physics, and engineering PLM majors. Those of you who are math, physics, engineering, and computer science, you need to do it the way I’m doing it in the Pllem Major book, the full circle. This is for the everyday average person. I I do multiple things for multiple people on here. [snorts] This is not cheating. I am just I’m showing you guys how to do this so that you can mimic it on your own and then stop watching videos basically. Okay. So, I’m going to take this now and I am going to get rid of the common denominator. All right. And so first thing I’m going to do then is I am going to embrace this in I’m going to parenthetical this parenthesis. I’m going to use square brackets and uh let me copy this again here. Copy this here. And then over here I am going to do another square bracket and do three parentheses x – a x – 1 x + a x – a. All right. Now I have my implication symbol there and that is uh in in there we go. So then this this is going to cross this is going to go through now and we you can if you want to now you can do this here put that here here and here and then I will take that out of the parenthesis now and then bring this down here and what we’ll see is the xus a will cross off and the x plus a will cross off so let me let me do that and I hope you guys see how fast and efficient using Microsoft off where it is for this latte and handwriting is not what you want to do. [snorts] All right. So, this is going to be two minus two times that part now. So, two times that. Okay. Now, now I need to foil all this out. I might want to look and see if there was any any faster way for me to do this. You know, there might have been a better way for me to go about this, but I’m already committed to this. So, I’m just going to go ahead and foil this out. Uh, I’ve already committed myself to this and foiling it will be fairly straightforward. Okay, this is going to be x^2 x^2 + ax – x – a. And it would be a good idea for you to remain in parentheses upon doing these so that if there’s any negative signs or numbers scalers that you have to distribute, you won’t miss those. So this is x^2 – ax – x + a. Uh and then this one is x^2 x^2 – a x + a x – a^ 2. Okay, assuming I didn’t make any typos along the way here, I can now remove this from the parenthetical from the parenthesis. I can get that out of the parenthesis. And then this one here, I can distribute two everywhere. This this obviously goes to zero here. So I get minus 2 a^2 here. Okay. Okay. So then that now I can take this piece here and I can get I got x^2 and x^2 and 2x^2. That’s all going to cancel off. Get out of there. Okay. So let me get these collect like terms. I got minus a minus a and plus a. That goes away. And then I got minus ax and plus ax. That goes away. – ax – x that wait – x – x that’s – 2x okay and so then here here I do that now now the two x’s these go away that goes away and that goes away and the negative the negative -2 goes away all right and so then to finalize thus x is equal to a^2. Okay. And that will conclude how you would write that and that matches with the answer. So we’ll go ahead and leave it like that. Okay. This is the uh college algebra. I’m I’m going to be doing just quick solutions to show you guys how it’s done for exams. There is multiple facets to what I do on here. I’m showing you how to strategize for exams. I’m also showing you how to understand math and physics through PLM Academy. So, uh, there’s different levels of education, different things that you guys need to do. Over here on Plym Academy, I show you guys how to do the full circle of math and give you guys a research position. We do it very in-depth, very intense, very elaborate, very long, very structured. Then, this is how you do exam questions. So, so the crash course series are just me doing exam questions. The other books are me writing in-depth elaborate solution methods for you guys. Okay? There’s different levels. I’m not trying to show you how to cheat here. I’m showing you how to site the book here. And this was 1.1. So a chapter 1 section one and then so 1.1 here. Uh I don’t necessarily need that 1.1 there. Uh well I suppose I’ll leave it there. So this is section one, chapter 1, section one, problem 73. I cite the book so that you know where the question comes from. So, I should put this actually right here so you know where the questions come from. And I’m just showing you quick solutions on this. Now, uh this is fine. I don’t need to organize anything. I can align these. If I want to align these, I can blah blah blah, but not a big deal. Okay, we’re just going to be I’m just going to be going through in sequence algebra trig pre-calc cal one in order starting at each each section and just kind of doing a crash course thing for each one of these things. All right, have a nice day.