Kuta Tutorial solving rational equations Part 2

welcome everyone to part two of rational equations in part one we talked about the step-by-step process first we try to find extraneous solutions then we eliminate fractions by multiplying by the least common multiple and then forgot to write step three which is solve so we're going to apply those same principles here in the second page of this worksheet and we're going to start with number 13. looks super complicated it really isn't that bad one thing you'll see is we have this trinomial expression in one of the fractions anytime you see something that you can factor it always makes sense to factor that first and you'll see right here have limited time have seven percent left battery so i'm gonna try to finish in before that time so i'm gonna put an here i'm gonna put an here for this particular fraction right here the numerator and this is gonna be think negative eight and plus three will be my numerator there now so if were to rewrite this it would look like that plus 3 and then 3x and then equals minus 6 over 3x now this is all about multiplying by the least common multiple of the denominators so that's what we're going to do next is multiply by 3x to all these terms so technically we're distributing this to all three terms and this is what it looks like we're gonna have let me write the one here and i'm probably gonna have to you can see have low battery i'm gonna have to get my charger really soon this battery change drains lot quicker than thought so then we have plus three that one times the three and then we have this minus eight times plus three and then we have that over three and this is equal to that minus 6 over 3x but can't forget about the 3x i'm going to put this in parentheses and now i'm ready to proceed so have everything ready here and now i'm just going to cancel don't cancel here any time you multiply it by non-fraction you're not going to cancel but here we're going to cancel so we're going to cancel all that and what are we left with we're left with 3x plus minus eight times plus three and really shouldn't have factored here just took chance and maybe could have factored but and that may have helped us and it really didn't so i'm gonna do here is i'm gonna erase and now i'm going to just write this out and get squared minus 5x minus 24 and really all need to do that for was this 3x and this negative 5x so get squared minus 2x minus 24 equals minus 6. any time you have an squared term and an term really want to get everything on one side and set it equal to zero so what i'm going to do here is i'm going to move over the and the minus six to the other side and we'll proceed from there so first i'm gonna subtract six then i'm gonna add six and as you can see got chargers that's what was doing so minus plus six get squared minus three and then that's minus 18 equals zero sorry about this don't there's not lot of room to write in this worksheet so now i'm going to factor this and then solve any what forgot to do forgot to check for extraneous solutions so we'll go ahead here we set 3x equal to zero so we say cannot be equal to zero we talked about that in the first video cannot be equal to zero so now we're back here to our solution we have and we need factors of negative 18 that add up to positive or negative three and that's going to be six and three with the six being negative and the being positive so then we get equals negative three and positive six we're gonna see that those solutions are not zero and they are not so we are good to go these are our two solutions here negative three and six the next one we're going to do is number 16. let's check for extraneous solutions first keep forgetting to do that step so we're gonna have squared minus two equals zero you always need to have it in factored form first so i'm going to factor out an and get minus 2 equals 0. so have equals cannot be equal to or cannot be equal to 0. 0 times whatever those parentheses would be zero and then times two minus two which is zero that would also give me zero so these are our extraneous solutions here all right so now i've found my extraneous solutions now what i'm going to do is i'm going to multiply by the least common multiple this is the part where it actually pays to factor put it into factored form first so i'm going to put this into factored form that's and then minus 2. we just did that to find the extraneous solutions minus 2 so i'm going to rewrite this problem as plus 5 over times minus 2 minus 1 equals 1 over times minus 2. my least common multiple only have one denominator so this actually is pretty easy i'm gonna multiply everything by minus two so i'm going to have minus let me actually move this up okay i'm gonna copy this should have done this earlier it's way easier way i'm going to copy and paste this and then i'm just going to write that i've distributed this minus 2 to the numerator here i'm right minus 2. put that in parenthesis 2. this gets multiplied by minus 2 and then this gets multiplied by minus 2. the whole point of doing that is so we could cancel out the denominators forgot to multiply by times minus 2 times minus 2 and then times minus 2. now we can cancel everything so the minus 2 gets cancelled and the gets cancelled in that fraction this doesn't cancel and this middle fraction or that's not even fraction this middle term this cancels and minus 2 cancels what are we left with we're left with plus five minus minus two times and then this is equal to one okay so now we just need to simplify so we have plus five minus plus two oops need to distribute first i'm so sorry didn't see that so can distribute this get minus distribute first so we get minus squared plus two equals one and i'm gonna get everything over to the left side so have don't like it when it's negative squared so actually i'm going to move everything over to the right side by adding the opposite so i'm going to have positive squared here i'm going to have minus three over here minus five and then plus the one that was already there and that's equal to zero now i'm gonna simplify little bit further squared minus three minus four and now it's time for parentheses so need factors of negative four that add up to pi negative three keep saying positive for some reason four one the four has got to be negative this is gonna be positive and have an and the equals zero so my answer is equals negative one and positive four need to check my extraneous solutions though it couldn't be two or zero so i'm good these are my solutions and now we're on to the last problem which is number 19. okay so we have we have lots of things going on here we have squared plus in the denominator and then plus one so really what i'm going to do is i'm going to factor this this is the same thing find my extraneous solutions first squared plus equals zero this gets factored to plus one so really we account for this plus one or extraneous solutions with this one because it's already present and so our external solutions cannot equal zero from this guy right here and then negative 1 from this guy so there's our extraneous solutions we'll check that at the end and now we're ready to proceed first i'm going to rewrite this problem as plus 5 over and i'm going to write it in the factored form times plus 1 equals 1 over times plus 1 minus minus 6 over plus 1. my least common multiple you'll see that have plus 1 in there so i'll need to multiply everything by plus 1 but also have that in this these two fractions so need to multiply it by once do that i'm going to copy and paste here copy paste and i'm going to add in my these common multiple to the tops of all these plus one times times plus five this numerator plus one times and then this last one plus one times okay time to cancel this is the best part this is why we chose to multiply by the least common multiple this cancels this plus 1 cancels cancels with plus 1 cancels with plus 1 and then this just has plus 1 to cancel what are we left with we're left with plus 5 equals everything canceled in this first one and then so that's gonna be one don't just write zero it's going to be one okay so we have one minus and then we have minus six times what i'm do is distribute first plus 5 equals 1 minus squared and that's going to be plus because we're distribute that negative sign 6p i'm going to get everything over to the left side because don't like it when the squared term the leading coefficient is negative so move everything over to the left i'm gonna add squared there i'm gonna subtract c6p and i'm gonna subtract one and already have and five already on the left side and it's equal to zero so have squared minus five plus four equals zero i'm into the final stage of the game here almost done and now we just have to factor it so we're gonna factor we have two parentheses here factors of positive four that add up to negative five that's gonna be negative four and negative one so equals one and negative four or positive four sorry what are our extraneous solutions our extraneous solutions were 0 and negative 1. it's negative 1 not positive 1 so this is good here 1 and 4 were our answers that's all there is to it this is the end of part 2. hope you enjoyed this video make sure you watch part one to understand little bit more of breakdown step by step of this process thank you so much for watching be sure to check out some of my other videos see you next time