Question 190243
{{{3/(4 - sqrt(7))}}} Start with the given expression.



{{{(3(4 + sqrt(7)))/((4-sqrt(7))(4+sqrt(7)))}}} Multiply both the numerator and denominator by {{{4+sqrt(7)}}}



{{{(3(4 + sqrt(7)))/(4^2 - (sqrt(7))^2)}}} FOIL the denominator (using the difference of squares)



{{{(3(4+sqrt(7)))/(16-7)}}} Square each term



{{{(3(4+sqrt(7)))/(9)}}} Combine like terms.



{{{(12+3*sqrt(7))/(9)}}} Distribute




So {{{3/(4 - sqrt(7))=(12+3sqrt(7))/(9)}}}