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# Intro to adding rational expressions with unlike denominators

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 we'll 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 the 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 BD, I multiplied
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, BC. BC over BD. 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 one, if we assume that D is not equal to zero, and then, if we just
multiply C over D times one, which is the same thing as B over B, if we assume that B is not equal to zero, then this fraction and this
fraction are equivalent. Now, why did I go through
all of this trouble? Well, now, I have a common denominator, so I can add these two fractions. So what's this going to be? Well, common denominator is BD, so let me just, so the
common denominator is BD, and I could just add the numerators, just like you would've
done if these were numbers, if this wasn't an algebraic expression. So this is going to
be, this is going to be AD plus BC, all of that over BD.