Confused -- image attached

elseif

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In the denominator, it starts as 2+2 sqrt 3.

... 2+2 = 4, of course.

Then before reducing the denominator and numerator by 2, it gets converted to 2*1 sqrt 3.

... But 2*1 = 2.

Why does this work? Would you help me to understand it? My brother was lost on this one too.

Thanks.
 

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pka

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Why does this work? Would you help me to understand it? My brother was lost on this one too.
Are you really asking why:
\(\displaystyle \frac{6x}{1+\sqrt{3}}=\frac{6x}{1+\sqrt{3}}\left(\frac{1-\sqrt{3}}{1-\sqrt{3}}\right)=\frac{6x(1-\sqrt{3})}{1-3}=?\)
If that is a mystery to you then you need to go back and study basic algebra.
 

elseif

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No.
I'm asking why 2+2 can be converted into 2(1).
 

Romsek

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No.
I'm asking why 2+2 can be converted into 2(1).
it's not \(\displaystyle 2+2\)

it's \(\displaystyle 2+2\sqrt{3}\)

The 2 then gets factored out from both terms

\(\displaystyle 2+2\sqrt{3} \Rightarrow 2(1 + \sqrt{3})\)
 

elseif

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it's not \(\displaystyle 2+2\)

it's \(\displaystyle 2+2\sqrt{3}\)

The 2 then gets factored out from both terms

\(\displaystyle 2+2\sqrt{3} \Rightarrow 2(1 + \sqrt{3})\)
Ah, I believe that I understand now. Thanks!
 

Harry_the_cat

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It's like 2 + 2x which isn't 4x.
 

hoosie

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Just in case you’re not sure I have given you an example to work through.
1F8F3B73-71DA-46D0-82EB-E0A04E7EE416.jpeg2C806086-B663-4BBA-A087-7B577AB034F7.jpeg
 

Otis

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… it starts as 2+2 sqrt 3 … 2+2 = 4, of course …
Hi elseif. We need to remember the Order of Operations.

2 + 2 × √3

We're not allowed to do the addition first.

😎
 

Jomo

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No.
I'm asking why 2+2 can be converted into 2(1).
Not sure why you are asking this for this problem but here id the answer.
2+2 = 4 while 2(1)=2. They are simply not the same.

Yes, 2+2 =4 but you have 2+2sqrt(3). The plus sign separates what you are adding! You are not adding 2 and 2 but rather 2 and 2sqrt(2).
Please watch this video
 
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