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

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Answer 1 · 2016-05-03T03:25:13

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

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
$(sqrt(x)+1) / [(sqrt(x)-1)*(sqrt(x)+1)] = (sqrt(x)+1) / (x-1)$

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