For what value of x is the function h above defined? What is undefined? Do you remember that? undefined just means you're dividing by zero. So they're asking you, when is H of X for what value of x does h of x is undefined. So basically, you're dividing by 01 over zero, the world explodes.

The universe explodes when you do that, okay? But for the SEC, they want to know for what x value is one over zero, the fact for h o h of x. So what you want to do is you want to equate the denominator to zero and figure out what that x will be. So let's write it here. x minus five squared plus four times x minus five plus four is equal to zero. Now, there is a very difficult way of doing this and you could waste a lot of time and I'm not going to go through it because I don't want to waste your time.

Now, the easiest way to do This is to recognize that this is written in a perfect square form. Don't believe me, we'll take a look. Let's say that x minus five, we're going to call that C. Okay? I'm just in the mood to call that C. So that's C, and this is also C. So if I rewrite this using C's, I will get c squared plus four times C, which I can just write SC plus four equals zero. Now, the C squared plus four c plus four can be written as c plus two squared. That is how we can use the perfect square.

Now again, you don't believe me, right? I know. You're like, No, well, I don't know how you got there. You went from that to that level of luck. Well, let's look at this. c plus two times c plus two, c times c squared.

Two See, and then two times see, well, that's two c plus two c plus two times two, that's four. So you get c squared plus four, c plus four. Now, we could have saved all that time, but you don't believe me. So here you go, c squared plus four c plus four. Nice. So then we can actually use this to calculate what the value of x is because it's really, really easy now, right?

So let's plug in our x, or our C and our C, remember we said was x minus five, so we have actually have x minus five plus two, right? Remember, C was just this guy right here. All of that squared equal to zero. I can simplify this further by doing x minus five plus two, well, negative five plus two is negative three. So x minus three squared is equal to zero. So then you can you can just stop right there.

Because what value of x is going to make the zero. Well, if x is three, three minus three is just zero. So there you go. For a value of three, this whole thing up there is undefined