How do you rationalize the denominator and simplify #1/(sqrtx-1)#?

1 Answer
Zor Shekhtman
May 3, 2016

#(sqrt(x)+1) / (x-1)# for #x>=0# anmd #x!=1#.

Explanation:

The domain of this function is:
#x>=0# to be able to perform an operation #sqrt(x)#,
#sqrt(x)-1 != 0#, that is #x != 1# to avoid division by #0#.

For all #x# satisfying the above criteria let's multiply both numerator and denominator by the same expression #(sqrt(x)+1)#.

This transforms our expression into
#(sqrt(x)+1) / [(sqrt(x)-1)*(sqrt(x)+1)] = (sqrt(x)+1) / (x-1)#

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