If, for non-zero real variables $x, y$, and real parameter $a>1$,
\[
x: y=(a+1):(a-1) \text {, }
\]
then, the ratio $\left(x^{2}-y^{2}\right):\left(x^{2}+y^{2}\right)$ is
- $2 a:\left(a^{2}+1\right)$
- $a:\left(a^{2}+1\right)$
- $2 a:\left(a^{2}-1\right)$
- $a:\left(a^{2}-1\right)$
