Answer: [tex]\bold{-7+2\sqrt{14}+5\sqrt{7}-10\sqrt{2}}[/tex]
Step-by-step explanation:
[tex]\dfrac{\sqrt7-5}{\sqrt7+\sqrt8}\bigg(\dfrac{\sqrt7-\sqrt8}{\sqrt7-\sqrt8}\bigg)=\dfrac{7-2\sqrt{14}-5\sqrt{7}+10\sqrt2}{7-8}=\dfrac{7-2\sqrt{14}-5\sqrt{7}+10\sqrt2}{-1}\\\\\\=\boxed{-7+2\sqrt{14}+5\sqrt{7}-10\sqrt2}[/tex]
