Question

if f(x)=square root of x^2-1 and g(x)=square root x-1, Which expression represents f(x)/g(x) for x>1?

Answer 1

`f(x) = \sqrt{x^(2) - 1}`

`g(x) = √(x - 1)`


`(f(x))/(g(x)) = \sqrt{(x^(2) - 1)/(x - 1)}`


`(f(x))/(g(x)) = \frac{\sqrt{x^(2) - 1}}{√(x - 1)}`


`(f(x))/(g(x)) = \frac{\sqrt{x^(2) + x - x - 1}}{√(x - 1)}`


`(f(x))/(g(x)) = (√((x - 1)(x + 1)))/(√(x - 1))`


`(f(x))/(g(x)) = √(x + 1)`

Answer 2

`f(x)=√(x^2-1),g(x)=√(x-1)`

Hence
`f(x)/g(x)=\sqrt{(x^2-1)/(x-1)}=\sqrt{((x+1)(x-1))/(x-1)}=√(x+1)`