expression

Question

If f(x)=square root x^2-1 and g(x)= square root x-1 f(x)/g(x) for x>1

Answer 1

f(x)/g(x) = (x² -1) / √(x - 1)

 

Rationalizing the denominator

 

f(x)/g(x) = (x² -1)( √(x - 1) )  / ( x - 1 )

 

Factoring the numerator

 

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

 

Reducing like terms

 

f(x)/g(x) = (x + 1)( √(x - 1) )