In Exercises 1–6, find all numbers that must be excluded from the...

Question

In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x−1)/(x^2+11x+10)

Accepted Answer

Welcome back. I'm so glad you're here. We've got this expression. I'm going to rewrite it. It's X squared minus nine divided by X squared minus five X plus six. And what are we doing here? We are going to figure out what numbers make this expression undefined And what does that mean? Well undefined would mean that we have a zero in the denominator and you just can't do that. You can't divide by zero, not allowed. So let's figure out what would give us a zero in the denominator in order to do that. We're going to take the denominator and we're going to set it equal to zero. We have X squared minus five, X plus six equals zero. And there are many different ways to figure out what our X values would be to make this true. And the one I'm going to look at here is factoring it. You could use the quadratic formula. Lots of different things. But so I'm going to say what times what gives us X squared? Well that's an X times an X. And what times what gives us a positive six but would add up to be a negative five. Well that would have to be a negative times a negative so that it equals a positive when multiplied and adds up to a negative number in what factors of six would add up to negative five. Well that would be a two and a three. We can do a really quick foil to check this out first X squared outside negative three X insides negative two X and lasts is a positive six combine like terms in the middle. Yes, this does match up. Great. So are correct factors are x minus two and x minus three. And now we can set each one of those equal to zero so that we can figure out what would give us zero in the denominator. So we can add two to both sides for x minus two and we get an X equals two. We can add three to both sides for x minus three. And that gives us an X equals three. And what does that tell us again? If we put a two in for X that would give us a zero in the denominator. Or if we put a three in for X, that would give us a zero in the denominator and we can't do that. That would make it undefined. We look at our answer choices and that matches with answer choice. A well done. We'll catch on the next one.

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