How To Add Rational Fractions With Unlike Denominators

let's take a look at adding or subtractingrational expressions. so rational expressions, it's sort of a strange word to many people,all it implies is that we have an exponent on the bottom - is that we have a variable,sorry, on the bottom. so like this, is the very simple kind of rational expression, herewould be a more involved rational expression. so these are both rational expressions, simplymeaning that there's a variable on the bottom

How To Add Rational Fractions With Unlike Denominators, of the fraction instead of just on the top.now if we wanted to add these two up, just like any time we add fractions, we need tomake sure that the denominators match up. so we have to get a common denominator here.so the common denominator just like you remember how if we do two thirds plus three fifths,one way to get a common denominator is to

say well, three times five is fifteen, we'regoing to do the same thing here, we're going to say x times x plus one is going to be ourcommon denominator. so i'm going to multiply, so i want to get - in order to get that commondenominator of x times x plus one, here, and here, just like you would with a normal fraction,you say what do i need to multiply by here, what i'm missing is this part. so i'm goingto multiply the bottom by that and the top by that. so what do i wind up getting? thistimes that is this, that's why we did it. two times x plus one is two x plus two, youdistribute, plus, now here, i already have this part, i just need that. so i'm goingto multiply the top and the bottom by x to give me this. x plus one times x is that.on the top i get three times x is three x,

now just like normal fractions, just likeadding normal fractions you carry the bottom over, this is your common denominator, soit's x plus one, and the top just like normal fractions. you add this plus that. so we'regoing to collect like terms. two x plus three x is five x and then the two doesn't havea common term, so we just copy it, final answer of this rational expression plus this one,five x plus two on the bottom, x times x plus one.