Explanation

Put U = x − a = (a² + 2ab + 5b²)/[4(a+b)] and V = y − b = (a² + 2ab − 3b²)/[4(a+b)]. Then U² − V² = (U − V)(U + V) with U − V = 8b²/[4(a+b)] and U + V = 2(a+b)²/[4(a+b)], giving 8b²·2(a+b)²/[16(a+b)²] = b² (B). A numeric check (a=2,b=1) also gives exactly 1.