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. 7/(x−3)

Accepted Answer

Welcome back. I'm so glad you're here. We've got this rational expression. I'll rewrite it. We have X divided by two X. Plus five. And we are to figure out what numbers make this expression undefined. What does that mean? Well an expression is undefined when it has a zero in the denominator you just can't do that. You can't divide anything by zero. So that is not allowed. So in order to find out what would make this undefined, it's like we have to be sneaky and we have to set the denominator equal to the one thing. It can't be. We have to set it equal to zero and then solve for X. That will give us any numbers that would make this undefined. So let's subtract five from both sides. Now we have two X equals negative five. Let's divide both sides by two. Now we have X equals negative five halves. And again what did that tell us? That tells us that if we stick a negative five halves in for X we would get a zero in the denominator and it would be undefined. So we look at our answer choices and that matches with answer choice B. Well done we'll catch on the next one.

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