Why is $|\sqrt{x} - \sqrt{c}|$ equal to $\frac{|x-c|}{|\sqrt{x} + \sqrt{c}|}$?

Question

How are these equal?

$$|\sqrt{x} - \sqrt{c}| = \frac{|x-c|}{|\sqrt{x} + \sqrt{c}|},$$

Answer 1

Because :

$$|\sqrt{x} - \sqrt{c}| = \frac{|\sqrt{x} - \sqrt{c}||\sqrt{x} + \sqrt{c}|}{|\sqrt{x} + \sqrt{c}|} = \frac{|(\sqrt x)^2 - (\sqrt c)^2|}{|\sqrt{x} + \sqrt{c}|} = \frac{|x-c|}{|\sqrt{x} + \sqrt{c}|} $$

Answer 2

Because $a^2-b^2=(a-b)(a+b)$. Apply this fact when $a^2=x$ and $b^2=c$.