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Question

If f(x)=√x^2-1 and g(x)=√x-1 what expression represents f(x)⁄g(x) for x>1.

Answer 1

Destiny, remember that if we have a square root in both the numerator and the denominator, you can instead put the radical over the entire fraction. 

 

√16/√4 = 4/2 = 2, or √16/√4 = √(16/4) = √4 = 2

 

So, now we have √[(x²-1)/(x-1)]

 

Remember that a^{2 -} b² = (a+b)(a-b).  This means we can factor x²-1 = (x+1)(x-1)

 

That gives us √[((x+1)(x-1))/(x-1)].  x-1 cancels out, so we have √(x+1) left.

 

Hope this helps!