Question 1040262
(12)/(6-√13) 
<pre><b>12 over 6 minus &#8730;13

{{{12/(6-sqrt(13))}}}

Form the conjugate of the two term denominator
by the rule: A+B and A-B are conjugates of each
other.

So the conjugate of {{{6-sqrt(13)}}} is {{{6+sqrt(13)}}}.

Then put the conjugate over itself, {{{(6+sqrt(13))/(6+sqrt(13))}}},
which equals 1, and since it equals 1, we can multiply
{{{12/(6-sqrt(13))}}} by it without changing its value.

{{{12/(6-sqrt(13))}}}{{{""*""}}}{{{(6+sqrt(13))/(6+sqrt(13))}}}

{{{(12*(6-sqrt(13)))/((6-sqrt(13))(6+sqrt(13)))}}}

FOIL out the bottom:

{{{(12*(6-sqrt(13)))/(36+6sqrt(13)-6sqrt(13)-13)}}}

{{{(12*(6-sqrt(13)))/(36+cross(6sqrt(13))-cross(6sqrt(13))-13)}}}

{{{(12*(6-sqrt(13)))/(36-13)}}}

{{{(12*(6+sqrt(13)))/23}}}

{{{expr(12/23)*(6+sqrt(13)))}}}

Either of the last two forms.

Edwin</pre></b>