If $$\frac{\sqrt{7}-1}{\sqrt{7}+1}-\frac{\sqrt{7}+1}{\sqrt{7}-1}=a+\sqrt{7} b$$ the values of a and b are respectively

$$\frac{\sqrt{7}-1}{\sqrt{7}+1}-\frac{\sqrt{7}+1}{\sqrt{7}-1}=a+\sqrt{7} b$$

L.H.S. = $$\frac{\sqrt{7}-1}{\sqrt{7}+1}-\frac{\sqrt{7}+1}{\sqrt{7}-1}$$

= $$\frac{(\sqrt{7}-1)^2 - (\sqrt{7}+1)^2}{(\sqrt{7}-1)(\sqrt{7}+1)}$$

= $$\frac{(7+1-2\sqrt{7})-(7+1+2\sqrt{7})}{7-1}$$

= $$\frac{-4\sqrt{7}}{6}$$

= $$\frac{-2\sqrt{7}}{3}$$

Now, comparing with R.H.S. $$a+\sqrt{7} b$$

we get,

$$a=0$$ and $$b=\frac{-2}{3}$$