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Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.$\frac{1}{\sqrt{x}+6}-\frac{2}{\sqrt{6}}$

$=\frac{\sqrt{x}-6}{x-36}-\frac{\sqrt{6}}{3}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 7

Rationalizing a Denominator

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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Rationalize the denominato…

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Rationalize each denominat…

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Simplify each expression. …

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So you have one over two squared of X plus six minus two over the square root of six. So whenever we subtract 20 common denominators, but it's gonna be hard to do that before rationalizing our denominators. So in order to rationalize, that means we just want to get rid of these square roots on the bottom. So the way to do that, it's multiplied by the contra git. So in this case, we have a plus B. So the contract is when we use the same two terms. But we put a subtractions on in the middle where you just wished, deciding. So whenever you oil everything else, you'll have a squared minus B squared. It's easier if you'd memorize this formula here instead of private a boil each time. It'll just make the problem solving much easier. Still, huh? We're X minus six over Route X minus six, your 1st 1 nor for extraction. And for a second fraction, we also need to get rid of this square. You end the denominator that was gonna multi part of the album bottom by the square root, cause we don't have any additional subtraction. Let me simplify this on the top floor for extraction will have one times through X minus six. And on the bottom will have room X squared minus six, clear and then minus in our second fraction. So we have to route six over six. Someone is simple for this. Further so far for instruction will have root. X minus six over and root expired. Will give us X Linus, and then six squared is 36 for a second fraction. We can reduce the top and bottom by two, but it becomes one and I becomes three. So we have this great of six over three now, in order to subtract thes two or we don't have to subtract, and we just needed to write him and simplest board. So this is our answer.

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