# 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 $$a+b+c$$?

×