Solving Rational Equations Easier Method

normally when they teach this technique in algebra classes is what they'll do is they'll say we'll find the common denominator and then multiply through by that common denominator to clear the denominators but often times students get little bit confused by that and so what I'm going to show you here is let's just see if we can get all the denominators to be the same okay so here you can see this has an this has five and this has 10 okay we want all these denominators to be the same so if we can make all these denominators 10 see because this one has an it's missing 10 right so if multiply that by 10 have to make sure do it to the top and the bottom so you can see have 10 * 3 over 10x now over here really need two and an to make this 10 okay so I'm going to multiply the top and bottom by 2X and then here I'm just missing an so I'm going to multiply the top and bottom by okay so now you can see that all the denominators are 10x so now what would do is would say all right I'm going to multiply everything by this denominator 10x so when you do that when you distribute it okay what happens is when you multiply the 10x and the 10x those are going to cancel so what it does is it clears the denominators you don't want to actually multiply the numerators by 10x you just want to realize that since these all have the same denominator if you were to multiply through by that common denominator you're just going to be left with the numerators so are you with me so far so we're just going to have those numerators once all the denominator are the same you can ignore those because they're going to cancel out if you multiply by that common denominator 10x so what we have here now is 30+ 4X = x^2 I'm just going to get everything on one side by subtracting 4X and subtracting 30 set that equal to zero now what you can do is you can try to factor it or you could do the quadratic formula or you could complete the square any of those techniques so that you can find out what is but the main thing is you want to make sure that the denominator is not zero so if in this case if came out to zero when we solve this then that means that it's no solution that's false answer or an extraneous solution so this would involve would probably do the quadratic formula now let's go over to example number two now this one what recommend doing first is factoring the denominator okay all the denominators so you can see what they're all composed of or what they're made up of right so you can see this one has an X+ 3 but it's missing an X+ one so what we're going to do is we're going to multiply by what it's missing so that it'll have the same denominator okay this one has an X+ one but it doesn't have an plus 3 see our goal is to get all the denominators to be the same okay so whatever it's missing multiply the top and bottom by that quantity now you can see okay they all have the same denominator so what you can do is you can ignore those denominators okay when say ignore don't mean ignore just mean that if you were to multiply through by the common denominator which is X+ 3 + 1 right X+ 3 and + 1 if you were to distribute this to each of these fractions because this is in the numerator and this is in the denominator it's going to cancel those out so effectively what we can do is focus just on the numerators at this point so what I'm going to do is I'm just going to distribute the four okay over here I'm going to distribute the and we're just focusing on those numerators so now it's little bit easier to solve because we don't have all those fractions let's get everything on one side and set it equal to zero okay so I'm just going to add two okay to make this equal to zero so we have x^2 + 7 cuz 4X and 3X right plus 6 so if we Factor this we get + 6 and + 1 and if we set those equal to zero we get -6 And1 now again you want to quickly check cannot be Nega 1 because 1 + 1 is zero we can't divide by zero that's undefined so we're going to cross that out that's extraneous whereas over here -6 is okay we just want to make sure doesn't come out to-3 or Nega 1 because again we' be dividing by zero that's undefined so hope this helped you understand how to work with solving rational equations better subscribe to the channel check out more math tutoring videos on my YouTube channel Mario's math tutoring and look forward to helping you in the future videos I'll talk to you soon