In Exercises 21–36, find the vertical asymptotes, if any, and the...

Question

In Exercises 21–36, find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. h(x)=(x+7)/(x^2+4x−21)

Accepted Answer

consider the given rational function and find vertical as um toasts and values X corresponding to holes. So we have X plus three over X squared minus two X minus 15. We want to determine our vertical ascent. Oh and Holtz these are just kind annuities. So they want to see if our equation has a discontinuity. Normally the way to find this continuity is by setting out to nominate equal to zero and solving for X. However we actually have a polynomial on the bottom that is quadratic. So we're gonna actually factor that out and see if we have common factors on the top and the bottom. And we're gonna simplify the equation. Let's try and do that first. So you have exposed three on top on the bottom, you have two factors X X 15. So I'm gonna say we have five and and we're gonna find our signs. We have a negative science. We have a plus and a minus. I'm gonna say minus five and plus three. So now we're here let's simplify it further. We have X plus three on the top, X plus three on the bottom. That gives us one over x minus five. So our simplification is one over X -5. So you want to determine what our vertical sm toad is now. So this continuity will be when we set our denominator equal to zero. So we will set X -5 equals zero. We did that, we get X equals five in that we have a vertical ascent At x equals five. Now, if you recall behind the common factor that was earlier, if we have a common factor, meaning a factor on the top and the factor on the bottom, that factor is actually a whole. So he said, X-plus three was our common factor. Since it's a common factor, we're gonna set X plus three equal to zero and solve for X principles negative three, meaning that we have a vertical ascent at X equals five and their whole at X equals negative three, which means the answer to our problem. It's answer. C. Okay, I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 21–36, find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. h(x)=(x+7)/(x^2+4x−21)

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