Question 139600
Not sure whether you mean {{{sqrt(a)/(sqrt(a)-2)}}} or {{{sqrt(a)/(sqrt(a-2))}}}  Either way, 'rationalize' means 'rationalize the denominator' and that means 'get that nasty radical out of my denominator'



{{{sqrt(a)/(sqrt(a)-2)}}}


You need to multiply the denominator by its conjugate, namely {{{sqrt(a)+2}}}, therefore you need to multiply the entire fraction by 1 in the form of {{{(sqrt(a)+2)/(sqrt(a)+2)}}}


{{{(sqrt(a)/(sqrt(a)-2))((sqrt(a)+2)/(sqrt(a)+2))}}}


The denominator becomes the difference of two squares, and you just distribute for the numerator:


{{{(a-2sqrt(a))/(a-4)}}}



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{{{sqrt(a)/(sqrt(a-2))}}}


Again, you need to multiply by 1, this time in the form of {{{sqrt(a-2)/sqrt(a-2)}}}, so:


{{{(sqrt(a)/(sqrt(a-2)))(sqrt(a-2)/sqrt(a-2))}}}


{{{(sqrt(a)sqrt(a-2))/(a-2)}}}


{{{(sqrt(a^2-2a))/(a-2)}}}