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# Multiplying rational expressions: multiple variables

CCSS.Math:

## Video transcript

multiply and express as a simplified rational state the domain so we'll start with the domain the the only numbers that will make this expression undefined are the ones that would make the denominator equal to zero and those are the situation or that situation would occur when either a be X or Y is equal to zero if any of those are equal to zero then we'll have we have an undefined expression so we could say that the domain the domain is all real is B's X and Y's except except 0 or we could be specific except except a b x and y can't equal to 0 or you could write maybe that maybe we write this given that a B X and Y does not equal 0 that none of them can be equal 0 that's these are just multiple ways of stating the same thing now with that stated let's actually multiply and simplify this rational expression so what we have is so when we multiply you just multiply the numerators multiply the denominator so you have 3x squared Y times 14 times 14 a squared B in the numerator and then in the denominator in the denominator we have 2 a B times times 18 X Y squared and let's see where we can simplify this thing well we can divide the 14 by 2 and the 2 by 2 and see what we get 14 divided by 2 is 7 2 divided by 2 is 1 and if we could divide the 3 by 3 and get 1 and divide the 18 by 3 and get 6 we do every time we divided the numerator denominator by 2 now the numerator is 1 and the denominator by 3 so we're not changing the expression and then we can divide a squared divided by a so you're just left with a you're just left with an a in the numerator and a divided by a is just 1 you have a B over B those guys cancel each other out you have an x squared divided by an X so x squared divided by X is X and X divided by X is just 2 1 so just becomes an x over 1 or just an X and finally have a Y over Y squared so if you divide the numerator by Y you get 1 you divide the denominator by Y you just get a Y so what are we left with we are left with in the numerator all we have these ones we can ignore that doesn't really change the number we have a 7 7 times a times X that's what we have in the numerator and in the denominator we just have a 6y 6y and we have to add the constraint that that a b x and y cannot equal 0 because when you just look at this expression right here you're like hey what's wrong with X or I mean there isn't even any be here so it's a little bit of a bizarre a statement but there's your say hey why can't X or ay be equal to zero over here there it doesn't make it undefined but in order for these to really be the same expressions they have to have the same domains or actually if you know if these were functions that equal them in order for that f of X to be equal to this f of X right over here you'd have to constrain the domain in a similar way so it's not like this is fundamentally a different expression if you allow X's and A's in this one you can't allow X's and A's for them to be really the same you have to put the same constraints on it