How To Add Subtract Fractions With Variables

- what i want to do in this video is really make sure that we feel comfortable manipulating algebraic expressionsthat involve fractions. so we'll start with somefairly straightforward ones. so let's say that i had, let's say i had

How To Add Subtract Fractions With Variables, a over b plus c over d, and if i actually wanted to add these things, so itis 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 acommon multiple of b and d. so we could rewrite this as two fractions, with the common denominator bd,

so, plus, bd, actually, letme 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 multipliedthe denominator by d, so let me multiply thenumerator by d as well, then i haven't changedthe value of the fraction, i'm just multiplying by d over d. so this is going to be atimes 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 thesecond fraction, c over d, to go from d to bd, we multiplied by b and so, if i multiplythe denominator by b, if i don't want to changethe value of the fraction, i have to multiply thenumerator by b as well. so let's multiply thenumerator 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 equivalentto 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 justmultiply 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 thisfraction are equivalent. now, why did i go throughall 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 thecommon denominator is bd, and i could just add the numerators,

just like you would'vedone if these were numbers, if this wasn't an algebraic expression. so this is going tobe, this is going to be ad plus bc, all of that over bd.