foreign Just One Last rational expression example before moving on to a different topic so this is a an example that actually comes up in calculus it's called a difference quotient and uh it's a useful example um there are two variables in it there's X and there's also h and there's this is our numerator which is itself is a difference of rational expressions and then there's just H at the bottom okay so we're going to do this part first the the numerator so this is an example where um the common denominator because we're subtracting two rational expressions we need a common denominator the common denominator is just a product of the X and the X plus h so we have x times X plus h and remember whenever you have a situation where there are no common factors in your in your two denominators so your product is your is your common denominator it's nice to use this little uh kind of formula if you will A over B minus C over D this is a D minus b c over BD which essentially corresponds to Simply multiplying the X up to the left numerator and the other denominator to the right numerator so what we're going to do is we're going to have one times x minus 1 times X plus h and this is your new numerator all over h and so we simplify the the upper numerator so we have x minus x minus H all over x times X plus h all over h now um the the upper numerator simplifies to just minus H over x times X Plus H all divided by h and this is equal to now so H here's a little it's a little bit of a trick H in the bottom this is the same as H over one any number or quantity is the same when you divide it by one so you have a you have a fraction over a fraction which you can convert into multiplication by flipping the denominator so instead of H over 1 you'll have 1 over H when you flip it and now you can see because everything is multiplication you can actually cancel terms the H and the H cancel we get negative 1 over X times X plus h okay so this is an example of a difference quotient it's a useful one also to be sure that you're comfortable with rational expressions so you can even you know after this video you could go home and or you're probably at home you could just try this out and see if you can do it yourself okay that's it for now and next video will be a different topic