Multiply or divide as indicated. [(x^2-5x-24)/(x^2-x-12)]/[(x^...

Question

Multiply or divide as indicated. [(x^2-5x-24)/(x^2-x-12)]/[(x^2-10x+16)/(x^2+x-6)]

Accepted Answer

Hello today we're going to be simplifying a complex fraction. So the complex fraction given to us is a squared plus five A plus six over a squared plus a minus six and all of that is going to be over two A squared plus three a minus two over a squared minus a minus two. Now this looks a little messy because of the amount of terms that we have. But one way that we can simplify the complex fraction is to multiply the numerator and denominator by the reciprocal of this denominator. Doing so the reciprocal is going to be a squared minus a minus two over two A squared plus three a minus two. And since we're multiplying this, denominator by the reciprocal, we need to multiply this numerator by the reciprocal as well. So the reciprocal again is going to be a squared minus a minus two over two A squared plus three a minus two. So the reason why we multiply the numerator and denominator by the reciprocal of the denominator is because this allows us to completely cancel the denominator to just one that is going to leave us with a squared plus five A plus six times a squared minus a minus two over a squared plus a minus six times two A squared plus three a minus two. Now we need to go ahead and simplify this numerator and denominator. One thing to note is that all these terms are here are all factory ble. So let's go ahead and factor our numerator than in the numerator we have a squared plus five A plus six. This is going to factor two A plus two Times a plus three and we have a squared minus a minus two. This is going to factor to a minus two times a plus one. Next let's go ahead and factor our denominator in the denominator we have a squared plus a minus six. This is going to factor to a minus two times a plus three and finally we have two a squared plus three a minus two. This is going to factor two to a minus one times a plus two. So let's go ahead and combine all the factors together. In the numerator we got factors of a plus two times a plus three times a minus two times a plus one. And all of that is going to be over a - Times a plus three Times two A -1 times a plus two. So one thing to note, we have a plus two in both the numerator and denominator. So we can go ahead and cancel out those quantities. We have an a -2 in both the numerator and denominator. So we can go ahead and cancel those quantities and we have a plus three in both the numerator and denominator. And those quantities will cancel out We are then left with a plus one over to a -1. And this is in the simplest form possible. So this is going to be our solution, which also means that the solution to this problem is going to be D. So I hope this video helps you to simplify complex fractions, and I'll go ahead and see you all in the next video.

Multiply or divide as indicated. [(x^2-5x-24)/(x^2-x-12)]/[(x^2-10x+16)/(x^2+x-6)]

Key Concepts

Factoring Polynomials

Rational Expressions

Simplifying Complex Fractions

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