Explanation

Put u = √(a+b), v = √(a−b), so x = (u−v)/(u+v). By componendo–dividendo, (1+x)/(1−x) = u/v = √((a+b)/(a−b)). Squaring and cross-multiplying gives (a−b)(1+x)² = (a+b)(1−x)². Expanding yields −2bx² + 4ax − 2b = 0, i.e. bx² − 2ax + b = 0: option A.