Answer:
[tex](\frac{f}{g})(x) = \sqrt{x + 1}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \sqrt{x^2 - 1[/tex]
[tex]g(x) =\sqrt{x - 1[/tex]
Required
Find [tex](\frac{f}{g})(x)[/tex]
[tex](\frac{f}{g})(x)[/tex] is calculated as:
[tex](\frac{f}{g})(x) = \frac{f(x)}{g(x)}[/tex]
This gives:
[tex](\frac{f}{g})(x) = \frac{\sqrt{x^2 - 1}}{\sqrt{x - 1}}[/tex]
Apply difference of two squares on the numerator
[tex](\frac{f}{g})(x) = \frac{\sqrt{x - 1}*\sqrt{x + 1}}{\sqrt{x - 1}}[/tex]
[tex](\frac{f}{g})(x) = \sqrt{x + 1}[/tex]
