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# Intro to adding rational expressions with unlike denominators

CCSS.Math:

## Video transcript

what I want to do in this video is really make sure that we feel comfortable manipulating algebraic expressions that involve fractions so let's start with some fairly straightforward ones so let's say that I had let's say I had a over B plus C over D and if I actually wanted to add these things so it is just one fraction how would I do that well what we could do is we could find a common denominator well over here we don't know what B is we don't know what D is but we know a common denominator is just going to be B times D that is going to be a common multiple of B and D so we could rewrite this as two fractions with a common denominator BD so plus BD actually let me color code it a little bit so a over B is going to be the same thing as what over BD well to get to BD I multiply the denominator by D so let me multiply the numerator by D as well then I haven't changed the value of the fraction I'm just multiplying by D over D so this is going to be a times D over B times D notice I could divide the numerator and the denominator by D and I'm going to get back to a over B and then we can look at the second fraction C over D to go from D to BD we multiplied by B and so if I multiply the denominator by B if I don't want to change the value of the fraction I have to multiply the numerator by B as well so let's multiply the numerator by B as well and it's going to be BC B C BC over B D this is C over D so what I have here in magenta this fraction is equivalent to this fraction I just multiplied it by D over D which we can assume is 1 if we assume the D is not equal to 0 and then if we just multiply C over D times 1 which is the same thing as B over B if we assume B is not equal zero then this fraction and this fraction equivalent now why did I go through all of this trouble well now I have a common denominator so I could add these two fractions so what's this going to be well common denominator is BD so let me just so common denominator is BD and I can just add the numerators just like you would have done if this was if these were numbers if these were not if this wasn't an algebraic expression so this is going to be this is going to be a d plus plus B C all of that over B D