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Question 10The equationX+3x2+3xhas" INO undefined values.Izive the smaller undefined value;...

Question

Question 10The equationX+3x2+3xhas" INO undefined values.Izive the smaller undefined value;

Question 10 The equation X+3 x2+3x has" INO undefined values.Izive the smaller undefined value;



Answers

If the denominator of a fraction is $x+3,$ for what value of $x$ is the fraction undefined?

So we do not want X to be zero if x zero. What that would mean is that whatever would be on top doesn't really matter. We'll put it up here because if you divide by zero, this cannot happen. This is not possible. Dividing by zero is undefined. And so, um, this is undefined when x zero

Today we are doing polynomial and rational inequalities. Here, we are given the expression for x minus three over X plus one Equals zero, and we are asked to determine what the values of X. The expression is undefined. The expression is undefined whatever the denominator equal zero, So we're going to take that denominator of X plus one and set it equal to zero, solving for X. We subtract one from both sides and we're left with X equals negative one, so for X equals negative one, the expression will be undefined.

We need to find the values that will make this rational expression undefined. Which means that the dump denominator would be zero, and that's not allowed. So to find those were gonna pull the denominator out. We don't care what's in the numerator, and we're gonna set this denominator equal to zero, and then we're gonna find the values of X that will make it that way. So because it's a quadratic, we're going to go ahead and factor it into to buy no meals. This will factor. We can break that first term down into three x and X. And if we break eight down into negative for and positive two when we foil, we'll get the the quadratic we started with. Now, the principle of zero products will let us set each of those factors equal to zero to solve for X. So now I'm going to solve each of these equations to solve this first equation. I'm gonna subtract two from both sides first. That's three. X equals negative too, that I'm gonna divide by three. I'm going to get X equals negative, too. Thirties. Let's close that to Lario. And if I saw the second equation for X by adding four tobel sides. I'm going to get X equals form. So because these are the two values that will make the denominator equal to zero, these are the two values at which this rational expression is undefined.

Bring asked to find what values of X make this expression undefined. So the big No no. When in math is X is dividing my zero right Can't divide by zero. So we want to find all values that have us dividing by zero. So we're dividing by X plus two and we're divided by X plus four. But we're also dividing by This is a whole And if this is equal to zero, then that's also dividing by zero. So if expose three is equal to zero, that's a problem too. So we're gonna set X Plus two equals zero We're gonna set X plus three equals zero and I guess that expose four equal to zero. So that gives us X equal the negative two x equal to negative three and X equal to negative four. So the three values of X that will make this function undefined are negative to negative three and negative four. That is our final answer


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