Unit 9 3 1 Solving Rational Equations Introduction and Simple Algebraic Solving

do you remember this from math 20-1 yeah actually you spent quite bit of time solving rational expressions in math 20-1 some huge ones as matter of fact which included all kinds of factoring and all kinds of other nonsense do yourself favor go over to the math 20-1 and it's just the very last few podcasts in the rational expressions section and watch those again watch the algebraic ones because they're really really cool i'm just going to really show you easily how we did this remember rational equation again is an equation that has to have variable in the denominator that's what makes it rational yeah no kidding so if we're going to do this algebraically here okay you have to remember couple things the first thing figure out the restrictions yes those non-permissible values they come back to haunt you one of the reasons why is because what happens if you solve this thing and one of your answers is non-permissible value well then you can't use that value can you so in other words that becomes do you remember this extraneous solution yes my goodness math 20-1 is coming back to haunt you isn't it okay now what are ways of solving this algebraically common denominator god that's got to be the easiest way to do it also sometimes if it's simple enough you could just cross multiply and solve for well heck you did that in grade five right but the entire thing is to solve for and then again like said before check against those non-permissible values for those extraneous ones those extraneous answers so if you solve this thing and you got two and three as possible answer and an npv is 2 guess what 2 is extraneous you can't use it graphically there's two ways of doing this graphically there's two one is yes just solve it like it was y1 y2 in other words you're going to have some sort of function over here equals to some sort of function over here let that be y1 let that be y2 and suddenly look for the intersects that makes things really really simple but now check this out also you can do this method number two graph it as single function what do mean by that well if you have something over here across an equal sign something over here take this guy and just bring it over which gives you this minus whatever that star was okay equaling to zero because that equals to zero remember that zero is was at one time so that means your equals to zero means that you're finding the intercepts and when you graph them look for the intercepts okay so let's do some of this i'm going to do one question i'm going to do it both algebraically and graphically i'm going to show you both graphical methods but i'm going to show you that in separate podcasts to keep the podcasts nice and short okay so first things first what can you do in situation like this so if you see situation like this right away notice that this can actually be over one this is nice and simple this is cross multiplication question but look what you forgot to do these yes plus six cannot equal to zero means that cannot equal to negative six watch out for that npv it's gonna bite ya be careful okay so let's cross multiply well that's easy one times sixteen think that's sixteen plus 6 times 4 minus okay so now we're going to have to do little bit of foiling here and the fact that this is kind of written weird you know what let's just foil it like we would normally foil so there's 4x over here would give you your minus squared this 6 times 4 of course is going to give you positive 24 and then finally 6 times gives you minus 6 combine some like terms here you end up and don't forget this whole thing still equals to 16. okay you have 16 equals to minus squared minus 6x and 4x gives you minus 2x plus 24. how convenient and pretty that works out to be now here's what i'm going to do then i'm going to take that 16 and bring it over to both sides here my goodness look at that that cancels out to give you zero that here cancels out to give you minus squared that's still minus two and this is going to give you positive eight now don't know about you but don't like factoring anything that has negative leading coefficient now there's two things you can do here you can multiply each one each side by negative one changing the size of both sides changing the signs of both sides or you can take this whole thing and bring it over to the other side and let it equal to zero whatever way you wanna do this algebraically in your mind go right ahead and do it so i'm just gonna say let's just do this nice and multiply both sides by negative one and look what happens the negative one times zero still zero this changes every sign over here to give you squared plus two minus eight my god you look how pretty that works out holy smokes now you can simply factor this one in your head right you got minus four plus two do not forget that this actually equals to zero okay no it should be plus four minus two that's what get for jumping the gun here plus four minus two don't forget the equal to zero you got plus four equals to zero that's where my equals to minus four came from was one step ahead of myself there well equals two cross reference this with your non-permissible values remember the non-permissible values we better go back here and check out what they were don't remember what they were there it is cannot equal to minus 6. so cannot equal to -6 that would complete the entire answer right there so this actually has two possible outcomes and equals to minus six that's beautiful now what want to show you in the next podcast here is want to show you how to do the two graphical methods so there's the algebraic one stay tuned for the graphical ones