Answer :
[tex]f(x)=\sqrt{x^2-1},g(x)=\sqrt{x-1}[/tex]
Hence [tex]f(x)/g(x)=\sqrt{\frac{x^2-1}{x-1}}=\sqrt{\frac{(x+1)(x-1)}{x-1}}=\sqrt{x+1}[/tex]
Hence [tex]f(x)/g(x)=\sqrt{\frac{x^2-1}{x-1}}=\sqrt{\frac{(x+1)(x-1)}{x-1}}=\sqrt{x+1}[/tex]
[tex]f(x) = \sqrt{x^{2} - 1} [/tex]
[tex]g(x) = \sqrt{x - 1} [/tex]
[tex]\frac{f(x)}{g(x)} = \sqrt{\frac{x^{2} - 1}{x - 1}} [/tex]
[tex]\frac{f(x)}{g(x)} = \frac{\sqrt{x^{2} - 1}}{\sqrt{x - 1}} [/tex]
[tex]\frac{f(x)}{g(x)} = \frac{\sqrt{x^{2} + x - x - 1}}{\sqrt{x - 1}} [/tex]
[tex]\frac{f(x)}{g(x)} = \frac{\sqrt{(x - 1)(x + 1)}}{\sqrt{x - 1}} [/tex]
[tex] \frac{f(x)}{g(x)} = \sqrt{x + 1} [/tex]
[tex]g(x) = \sqrt{x - 1} [/tex]
[tex]\frac{f(x)}{g(x)} = \sqrt{\frac{x^{2} - 1}{x - 1}} [/tex]
[tex]\frac{f(x)}{g(x)} = \frac{\sqrt{x^{2} - 1}}{\sqrt{x - 1}} [/tex]
[tex]\frac{f(x)}{g(x)} = \frac{\sqrt{x^{2} + x - x - 1}}{\sqrt{x - 1}} [/tex]
[tex]\frac{f(x)}{g(x)} = \frac{\sqrt{(x - 1)(x + 1)}}{\sqrt{x - 1}} [/tex]
[tex] \frac{f(x)}{g(x)} = \sqrt{x + 1} [/tex]
