Here we want to multiply the fraction by its conjugate, thus:
\(\frac{10\sqrt{7}}{-1+\sqrt{10}} \times \frac{1+\sqrt{10}}{1+\sqrt{10}}=\frac{10\sqrt{7}(1+\sqrt{10}}{(-1+\sqrt{10})(1+\sqrt{10})}\)
expanding the denomenator comes out as 9. after expanding we get the following
\(\frac{10\sqrt{7}+10\sqrt{70}}{9}=\frac{-10\sqrt{7}-10\sqrt{70}}{-9}\)
I hope this helped :)