Multiply or divide as indicated. [(x^2+6x+9)(x+3)]/[(x^2-4)(x-2)]

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Hello today we're going to be simplifying irrational expression. So the rational expression given to us is X squared plus two X plus one. And that's gonna be multiplied by x minus one. And all of that is going to be over X squared minus one times X plus three. Now looking at the numerator this quantity is fact herbal and in the denominator x squared minus one is a difference of squares. So in order to reduce the numerator we need to go ahead and factor X squared plus two X plus one. This is going to factor two, X plus one times X plus one and x squared minus one is a difference of squares. Recall that the difference of squares is a squared minus B squared will factor to a plus B times a minus B. So that means that x square minus one is going to factor two X plus one times X minus one. So let's go ahead and plug in our new factors in the numerator we're going to have X plus one times X plus one times X minus one. And in the denominator we're going to have X plus one times X minus one times X plus three. Now, in order to simplify this, Notice that we have X -1 in both the numerator and denominator so we can go ahead and cancel those quantities. Next we have an instance of X -1 in the numerator and the denominator and we have two of them in the numerator. So we can go ahead and cancel one of them for the numerator and cancel the one in the denominator. And that is going to leave us with X plus one over X plus three. And that is the simplest form of this. So this is going to be our solution. That also means that the solution to this problem is going to be D. So I hope this video helps you simplify rational expressions and I'll go ahead and see you all in the next video.

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