Usuwamy niewymierność z mianownika ułamka. 

$\frac{4}{1-\sqrt{2}+\sqrt{3}}=\frac{4}{\left(1-\sqrt{2}\right)+\sqrt{3}}\cdot \frac{\left(1-\sqrt{2}\right)-\sqrt{3}}{\left(1-\sqrt{2}\right)-\sqrt{3}}=\frac{4\left(\left(1-\sqrt{2}\right)-\sqrt{3}\right)}{\left(\left(1-\sqrt{2}\right)+\sqrt{3}\right)\left(\left(1-\sqrt{2}\right)-\sqrt{3}\right)}=\frac{4\left(1-\sqrt{2}-\sqrt{3}\right)}{{\left(1-\sqrt{2}\right)}^2-{\left(\sqrt{3}\right)}^2}=\frac{4\left(1-\sqrt{2}-\sqrt{3}\right)}{1-2\sqrt{2}+2-3}=\frac{4\left(1-\sqrt{2}-\sqrt{3}\right)}{-2\sqrt{2}}=\frac{2\left(1-\sqrt{2}-\sqrt{3}\right)}{-\sqrt{2}}=\frac{-2\left(1-\sqrt{2}-\sqrt{3}\right)}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{-2\left(1-\sqrt{2}-\sqrt{3}\right)\sqrt{2}}{{\left(\sqrt{2}\right)}^2}=\frac{-2\left(1-\sqrt{2}-\sqrt{3}\right)\sqrt{2}}{2}=-\left(1-\sqrt{2}-\sqrt{3}\right)\sqrt{2}=\left(-1+\sqrt{2}+\sqrt{3}\right)\cdot \sqrt{2}=\sqrt{2}\cdot \left(\sqrt{3}+\sqrt{2}-1\right)$  

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Prawidłowa odpowiedź to C.