# Confused -- image attached

#### elseif

##### New member
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

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

#### elseif

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

#### Romsek

##### Full Member
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

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

• JoeyW and elseif

#### elseif

##### New member
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

##### Senior Member
It's like 2 + 2x which isn't 4x.

• elseif

#### hoosie

##### Junior Member
• Subhotosh Khan and elseif

#### Otis

##### Senior Member
… 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

##### Elite Member
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).