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+5)/(x^2−25)

Accepted Answer

Welcome back. I'm so glad you're here. We've got this rational expression. I'll rewrite it. We have x minus six in the numerator and x squared minus three in the denominator. And we're to write all the numbers that make this expression undefined and what does that mean? Exactly? What is an undefined expression? That's one that has a zero in the denominator because you just can't do that, you can't divide anything by zero, not allowed. So in order to find out what would give us a zero in the denominator, it's like we have to be sneaky and we have to set the denominator, X squared minus three equal to zero and then solve for X to see what numbers would give us a zero in the denominator. So for this one let's add three double sides. So now we've got X squared equals three. We can take the square root of both sides. So now we've got X equals plus or minus the square root of three. Or in other words X equals positive square root of three or negative square root of three. And what does this mean if we put a square root of three or a negative square root of three in for X we have a zero on the denominator and it would be undefined, we look at our answer choices and this matches answer choice. A Well done. We'll catch on the next one

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