Question 298086
{{{ (X-25)/(sqrt(X)-5) }}}


Multiply numerator and denominator by the conjugate of the denominator, which is {{{(sqrt(x) + 5)}}}.  However, when do NOT multiply out the numerator!  If you leave the numerator in factored form, then the x-25 factor divides out, like this:

{{{ ((X-25)/(sqrt(X)-5))*((sqrt(x)+5)/(sqrt(x)+5)) }}}

{{{((x-25)*(sqrt(x)+5))/(x-25)}}}


Now, the {{{(x-25)}}} divides out, and the final answer is 
{{{sqrt(x)+5}}}


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida