Multiple Choice 1 point If \( f(x)=\sqrt{x^{2}-1} \) and \( g(x)=\sqrt{x-1} \) which expression represents \( \frac{f(x)}{g(x)} \) for \( \mathrm{X}>1 \)

To simplify the expression \(\frac{f(x)}{g(x)}\) where \( f(x) = \sqrt{x^{2} - 1} \) and \( g(x) = \sqrt{x - 1} \) for \( x > 1 \), follow these steps: \[ \frac{f(x)}{g(x)} = \frac{\sqrt{x^{2} - 1}}{\sqrt{x - 1}} \] Factor \( x^{2} - 1 \): \[ x^{2} - 1 = (x - 1)(x + 1) \] Substitute back into the expression: \[ \frac{\sqrt{(x - 1)(x + 1)}}{\sqrt{x - 1}} = \frac{\sqrt{x - 1} \cdot \sqrt{x + 1}}{\sqrt{x - 1}} = \sqrt{x + 1} \] **Answer:** The expression simplifies to the square root of (x + 1), that is \(\sqrt{x + 1}\).