Question 93983
{{{(sqrt(x)+2)/(sqrt(x)-1)}}} Start with the given expression


{{{((sqrt(x)+2)/(sqrt(x)-1))((sqrt(x)+1)/(sqrt(x)+1))}}}  Multiply the fraction by {{{(sqrt(x)+1)/(sqrt(x)+1)}}} (which is a form of 1). This will rationalize the denominator.



{{{(sqrt(x)+2)(sqrt(x)+1)/(sqrt(x)-1)(sqrt(x)+1)}}} Combine the fractions



{{{(sqrt(x)sqrt(x)+sqrt(x)+2*sqrt(x)+2)/(x+sqrt(x)-sqrt(x)-1)}}} Foil the numerator and the denominator 




{{{(sqrt(x)sqrt(x)+sqrt(x)+2*sqrt(x)+2)/(x+cross(sqrt(x)-sqrt(x))-1)}}} Notice the root terms cancel in the denominator. Now the denominator is completely rational.



{{{(x+sqrt(x)+2*sqrt(x)+2)/(x-1)}}} Multiply {{{sqrt(x)sqrt(x)}}} to get {{{x}}}



{{{(x+3*sqrt(x)+2)/(x-1)}}} Combine like terms