rationalize-the-denominator-and-write-each-fraction-in-simplest-form-all-variables-represent-posi-34

Question

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

M S · Accepted Answer

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&#x27;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&#x27;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&#x27;ll have a squared minus B squared. It&#x27;s easier if you&#x27;d memorize this formula here instead of private a boil each time. It&#x27;ll just make the problem solving much easier. Still, huh? We&#x27;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&#x27;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&#x27;t have to subtract, and we just needed to write him and simplest board. So this is our answer.

Ashley Volpe · Answer

question Number 10 asked me to rationalize and simplify this expression I like to simplify first. So radical 12 is actually radical. Four times radical. Three radical four is too. So we really have six over to radical three six over to can simplify to 3/1. And so I have three over radical three that I need to now rationalize. If I&#x27;m gonna rationalize, I need to remove the radical from the denominator. And so we&#x27;re gonna do that by multiplying the numerator and the denominator by radical three radical three times Radical Three is gonna be radical. Non. And on the top, I&#x27;m gonna have three radical three radical non is just three. And then I noticed the three and three top and bottom are gonna cancel out. And so my final answer then that I&#x27;m gonna be left with It&#x27;s just gonna be radical. Three

Ashley Volpe · Answer

all right. So if they want us to rationalized and simplify this, we noticed there&#x27;s a binomial. So we&#x27;re gonna multiply by the conjugated now in the numerator. Of course, this is going to give us a distributive property problem. So six times three is 18 and six times negative radical. Three is gonna be negative. Six radical three in the denominator. We have a binomial times about no meals. So we&#x27;re gonna foil three times three is none. Three times negative. Radical. Three is negative. Three radical three, Three times positive. Radical. Three is positive. Three radical three and positive times. Negative. Makes this negative. Radical non at the end. Doing any simplification. We noticed that negative and positive three radical three will cancel out. Radical Non is just three. And so our denominator becomes non minus three. Cleaning this up and rewriting our problem. Our numerator is still 18 minus six. Radical three. Our denominator non minus 36 Now we&#x27;ve rationalized it, but we need to make sure it&#x27;s simplified. We have a coefficient of six a six and 18. Those air all divisible by six. 18. Device by six to get three 60 votes by six to get one on there in top and bottom. Since my denominator is one, I&#x27;m not going to have a denominator, But I am going to rewrite my numerator. And so I&#x27;m gonna end up with three monness Radical three as my final answer simplified and rest allies.

Ashley Volpe · Answer

okay. They want us to rationalize and simplify this. I like to simplify. So radical. 24. I&#x27;m gonna rewrite that as radical for Tom&#x27;s radical six. Um And so what that&#x27;s gonna give me, then, is radical four times radical six over to radical six. Now, that shows me that the top and the bottom have a factor of radical six, so I can remove those that&#x27;s gonna give me radical four over to. Well, radical four is just too, and to over two is gonna simplify down just one.

Amy Jiang · Answer

Okay, so we want to rationalize the denominator. So we want to get rid of the square root so we&#x27;ll multiply and divided by the square root of six. So this gives us six or describe it of 6/6.

Jeyasree R T · Answer

consider the human expression relation eyes the denominator went to great the new Britain and you know, major by squared off. So we get six square fine. Why don&#x27;t I find into squad? Don&#x27;t fight. It simplifies to six inches square fine by fine.

Problem

Rationalize the denominator and write each fracti…

Problem 36 Hard Difficulty

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

Answer

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

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry