Question

If `(sqrt(1 + x) + sqrt(1 - x))/(sqrt(1 + x) - sqrt(1 - x)) = a/b`, then x equals ______.

Options

• `a^2/(a + b)`

• `b^2/(a + b)`

• `(ab)/(a^2 + b^2)`

• `(2ab)/(a^2 + b^2)`

Answer 1

If `(sqrt(1 + x) + sqrt(1 - x))/(sqrt(1 + x) - sqrt(1 - x)) = a/b`, then x equals `underlinebb((2ab)/(a^2 + b^2))`.

Explanation:

Applying componendo and dividendo gives `sqrt((1 + x)/(1 - x)) = (a + b)/(a - b)`.

Squaring and rearranging yields `x = (2ab)/(a^2 + b^2)`.