`5/(sqrt(7)+\sqrt{2)}+1/(sqrt(2)-1)-7/(sqrt(7))`
`=(\sqrt{7}-\sqrt{2})+\frac{1}{\sqrt{2}-1}-\sqrt{7}`
`=\sqrt{7}-\sqrt{2}-\sqrt{7}+\frac{1}{\sqrt{2}-1}`
`=-\sqrt{2}+\frac{1}{\sqrt{2}-1}`
`=\frac{-\sqrt{2}(\sqrt{2}-1)}{\sqrt{2}-1}+\frac{1}{\sqrt{2}-1}`
`=\frac{-\sqrt{2}(\sqrt{2}-1)+1}{\sqrt{2}-1}`
`=\frac{-1+\sqrt{2}}{\sqrt{2}-1}`
`=1`