Question 115680
{{{5/(3-2sqrt(6))}}} Start with the given expression



{{{(5/(3-2sqrt(6)))((3+2sqrt(6))/(3+2sqrt(6)))}}} Multiply the fraction by {{{(3+2sqrt(6))/(3+2sqrt(6))}}}. Note: {{{3+2sqrt(6)}}} is the conjugate of the denominator




{{{5(3+2sqrt(6))/((3-2sqrt(6))(3+2sqrt(6)))}}} Combine the fractions



{{{(15+10sqrt(6))/((3-2sqrt(6))(3+2sqrt(6)))}}} Distribute



{{{(15+10sqrt(6))/(9+6sqrt(6)-6sqrt(6)-4sqrt(6)sqrt(6)))}}} Foil




{{{(15+10sqrt(6))/(9+6sqrt(6)-6sqrt(6)-4(6)))}}} Multiply



{{{(15+10sqrt(6))/(9-4(6)))}}} Combine like terms



{{{(15+10sqrt(6))/(9-24))}}} Multiply



{{{(15+10sqrt(6))/(-15))}}} Subtract



{{{(15)/(-15)+(10sqrt(6))/(-15))}}} Break up the fraction



{{{-1-2sqrt(6)/3)}}} Reduce