In Exercises 69–82, simplify each complex rational expression. (x...

Question

In Exercises 69–82, simplify each complex rational expression. (x/3−1)/(x−3)

Accepted Answer

Welcome back. I'm so glad you're here. We have this expression we have three divided by y minus X divided by y squared all over x minus three Y. Well where do we even start with this thing? Let's start with our fraction in the numerator. And let's combine those. So we're going to multiply this 1st 13 over Y times Y over Y because Y over Y is just one but that will give us a common denominator. So now we'll have three Y over Y squared minus X over y squared divided by x minus three Y. And now we can combine the numerator in our numerator. So we'll have three Y minus X over Y squared divided by x minus three Y. Now I'd like to rewrite this as three y minus X divided by y squared. And a division symbol like this divided by x minus three Y. Because this reminds me that it's the same thing as three, Y minus X divided by y squared times one over x minus three. Y multiplying by the second terms, reciprocal. So now it would be nice to just multiply straight across, see if we've got any common factors but we look at it and two of these factors are very, very similar. In fact they're basically in verses of each other three y minus x and x minus three Y. So let's multiply this second term, this one over X minus three Y times negative one over negative one because negative one over negative one, that's one. So we're just multiplying it by one. Now we can rewrite this as three y minus X over Y squared times a negative one over negative X plus three Y. And now let's rewrite this denominator so that the three Y goes 1st 1st copying everything over, we've got three y minus X over Y squared times negative one over now. Three y minus X. And there we go. We've got these two factors which will cancel each other out and now it's just a one here and one here and we can multiply straight across one times negative one. That's negative one. Why squared times one. That is why squared so we've got negative one over y squared. We look at our answer choices and that matches with answer choice. B. Well done. We'll catch you on the next one.

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