Question 92184
A.) {{{(sqrt(a) + sqrt(b)) / (sqrt(a) - sqrt(b))}}}
It can be simplified by getting rid of the radicals in the denominator
To do this, multiply it by the conjugate of the denominator: {{{(sqrt(a)+sqrt(b))/(sqrt(a)+sqrt(b))}}}
Any expression over itself, is one, so we are not changing anything, right?
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FOIL
{{{(sqrt(a)+ sqrt(b))/(sqrt(a)- sqrt(b))}}}* {{{(sqrt(a)+sqrt(b))/(sqrt(a)+sqrt(b))}}} = {{{(a + sqrt(ab) + sqrt(ab) + b)/(a - sqrt(ab) + sqrt(ab) - b)}}}
:
combine the middle terms in the numerator, the middle terms in the denominator
 cancel, getting rid of the radicals.
{{{(a + 2*sqrt(ab) + b)/(a - b)}}}
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(B.) {{{(sqrt(5)+1)/(sqrt(5)-1))}}}
Follow the same procedure, multiply by the conjugate of the denominator:
FOIL
{{{(sqrt(5)+1)/(sqrt(5)-1))}}} * {{{(sqrt(5)+1)/(sqrt(5)+1))}}} = {{{(5 + sqrt(5) + sqrt(5) + 1)/(5 - sqrt(5) + sqrt(5) + 1)}}} = {{{(5 + 2sqrt(5) + 1)/(5 - 1)}}} = {{{(6 + 2sqrt(5))/(4)}}}
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Note that this fraction can be reduced, divide each term by 2 and you have 
{{{(3 + sqrt(5))/2}}}
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Could you follow this OK? Any questions