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math question

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


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1 Answer

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.