# 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 \(a+b+c\)?