Question 117919
{{{(3+sqrt(7))/(1-sqrt(3))}}} Start with the given expression



{{{((3+sqrt(7))/(1-sqrt(3)))((1+sqrt(3))/(1+sqrt(3)))}}} Multiply by the fraction by {{{(1+sqrt(3))/(1+sqrt(3))}}}. Note  {{{1+sqrt(3)}}} is the conjugate of {{{1-sqrt(3)}}}.



{{{((3+sqrt(7))(1+sqrt(3)))/((1-sqrt(3))(1+sqrt(3)))}}} Combine the fractions



{{{((3+sqrt(7))(1+sqrt(3)))/(1*1+1(-sqrt(3))-(-sqrt(3))*1+(-sqrt(3))(-sqrt(3)))}}} Foil the denominator



{{{((3+sqrt(7))(1+sqrt(3)))/(1*1+(-sqrt(3))(-sqrt(3)))}}} Cancel like terms



{{{((3+sqrt(7))(1+sqrt(3)))/(1-3)}}} Multiply



{{{((3+sqrt(7))(1+sqrt(3)))/(-2)}}} Combine like terms




{{{((3)(1)+(3)(sqrt(3))+(sqrt(7))(1)+(sqrt(7))(sqrt(3)))/(-2)}}} Foil the numerator




{{{(3+3sqrt(3)+sqrt(7)+sqrt(21))/(-2)}}} Multiply