Question 317291
{{{(2sqrt(3)+4)/(-2sqrt(3)+5)}}}
<pre><b>
Put parentheses around the numeratior and denominator:

{{{((2sqrt(3)+4))/((-2sqrt(3)+5))}}}

Form the conjugate of the denominator by changing the
sign of the second term, that is, {{{(-2sqrt(3)-5)}}}, put it over
itself, {{{((-2sqrt(3)-5))/((-2sqrt(3)-5))}}}, which has value 1.
So we may multiply it by the original without changing the value

{{{((2sqrt(3)+4))/((-2sqrt(3)+5))}}}{{{"×"}}}{{{((-2sqrt(3)-5))/((-2sqrt(3)-5))}}}{{{"="}}}{{{((2sqrt(3)+4)(-2sqrt(3)-5))/((-2sqrt(3)+5)(-2sqrt(3)-5))}}}{{{"="}}}{{{
(-4*3-10sqrt(3)-8sqrt(3)-20)/(4*3+10sqrt(3)-10sqrt(3)-25)

}}}{{{"="}}}{{{-12-18sqrt(3)-20)/(12-25)}}}{{{"="}}}{{{(-32-18sqrt(3))/(-13)}}}

That's what you got but you can simplify it by multiplying by {{{(-1)/(-1)}}}

{{{(-1)/(-1)}}}{{{"×"}}}{{{((-32-18sqrt(3)))/((-13))}}}{{{"="}}}{{{(32+18sqrt(3))/13}}}

Edwin</pre>