Step-up Rationalization

Algebra Level 2

\[ \dfrac{\left( \sqrt2-1\right)^{1-\sqrt3}}{\left( \sqrt2+1\right)^{1+\sqrt3}} \]

If the expression above can be simplified to the form of \(a-b\sqrt c\), where \(a\),\(b\), and \(c\) are positive integers with \(c\) square-free.

What is the value of \(a+b+c\)?

Image Credit: Wikimedia Trigonometry Triangle by Limaner
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