Nested GCD simplification

Question

Let us assume two given co-prime integers $a$ and $b$. Let $d$ be another integer and $x_1$ and $x_2$ be two variables. Then is it possible to simplify this nested GCD expression $gcd\bigg(\frac{(x_1^2-d)(a^2-d b^2)}{gcd(a^2-d b^2; a-bx_1)};b(x_1 x_2-d)+a(x_1-x_2)\bigg)$? The question was due to my digging of some properties of gcds and co-primes.