math question

Question

If f(x) = sqrt(x^2-1) and g(x) = sqrt(x-1), which expression represents f(x)/g(x) for x>1?


Can you do the above problem and provide the answer?

Answer 1

If f(x) = √(x^2-1) and g(x) = √(x-1), then,

 

for x>1, f(x)/g(x) = √(x^2-1)/√(x-1)

 

= √((x^2-1)/(x-1)) = √((x+1)(x-1)/(x-1)) 

 

= √(x+1), x>1.