In Exercises 123–124, list all numbers that must be excluded from...

Question

In Exercises 123–124, list all numbers that must be excluded from the domain of each rational expression.

3/(2x^2 + 4x - 9)

Accepted Answer

Welcome back. I'm so glad you're here. We've got this expression five divided by X squared minus seven. X plus six. We want to figure out all the values of X. That will make this expression undefined. What does that mean? All the values of X. That would make this have a zero in the denominator. That would make it undefined. So to check for that, what we're going to do is we're going to take the denominator X squared minus seven X plus six. We're going to set it equal to zero exactly what it's not supposed to be. In order to find out what values would make it zero. What values of X would make it zero in the denominator and therefore undefined. Okay to figure out the values of X. What we're going to do for this equation is factor it. So what times what gives us X square that's going to be X times X. And what two numbers when multiplied give us a positive six. But when added give us a negative seven, that's going to be -6 -1. And now we can set both of those equal to zero. X minus six equals zero and X minus one equals zero. With both of those factors equal to zero. Will know which values for X. Will give us an undefined expression let's add six to both sides. So that will give us X equal six. Or in other words X can't equal six. If we add one to both sides for X minus one equals zero. That'll give us an X equals one. Or in other words X can equal one, or this will be undefined. We look at our answer choices in this matches answer choice D. Well done, we'll catch you on the next one.

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