Help Simplifying / Transitioning Expression to Alternate Form

[Pdunk250]

I am currently working through a problem and am not sure how I was supposed to simplify the expression.
The expression was originally [math]\sqrt{x+2}-\sqrt{x}[/math] and was converted to [math]\left(\frac{2}{(\sqrt{x+2}+\sqrt{x}}\right)[/math] . I just need help understanding how they converted to this.

 

[Zermelo]

I am currently working through a problem and am not sure how I was supposed to simplify the expression.
The expression was originally [math]\sqrt{x+2}-\sqrt{x}[/math] and was converted to [math]\left(\frac{2}{(\sqrt{x+2}+\sqrt{x}}\right)[/math] . I just need help understanding how they converted to this.

Multiply everything by [math] \frac{\sqrt{x+2}+\sqrt{x}}{\sqrt{x+2}+\sqrt{x}} [/math]. It’s the same as multiplying it by 1, nothing changes

 

[Shiloh]

"Rationalize the numerator". Think of this as \(\displaystyle \frac{\sqrt{x+ 2}+ \sqrt{x}}{1}\) and multiply by \(\displaystyle \frac{\sqrt{x+2}+ \sqrt{x}}{\sqrt{x+2}+ \sqrt{x}}\)
The numerator will be

\(\displaystyle (\sqrt{x+ 2}+ \sqrt{x})(\sqrt{x+ 2}- \sqrt{x})= (\sqrt{x+ 2})^2- (\sqrt{x})^2= x+ 2- x= 2\)

 

[pka]

I am currently working through a problem and am not sure how I was supposed to simplify the expression.
The expression was originally [math]\sqrt{x+2}-\sqrt{x}[/math] and was converted to [math]\left(\frac{2}{(\sqrt{x+2}+\sqrt{x}}\right)[/math] . I just need help understanding how they converted to this.

Surely in beginning algebra you did the product of a sum & difference ?
[imath] (a+b)( a-b)=~?[/imath]