Question 211185
Rationalize the denominator:
{{{(4-sqrt(3))/(6+sqrt(y))}}}
<pre><font size = 4 color = "indigo"><b>
That is, change the form of the fraction so that 
there are no irrational square roots radicals on
the bottom, but are all on top.

Form the conjugate of the denominator, which is
just like it except the sign of the second term
is changed.  So the conjugate of {{{6-sqrt(y)}}}
is {{{6+sqrt(y)}}}.  Multiplying the top and bottom
by that will not change the value of the fraction:

{{{(  (4-sqrt(3))(6-sqrt(y))   )/(  (6+sqrt(y))(6-sqrt(y))  )

= (24-4sqrt(y)-6sqrt(3)+sqrt(3y))/(36-6sqrt(y)+6sqrt(y)-(sqrt(y))^2)=

 (24-4sqrt(y)-6sqrt(3)+sqrt(3y))/(36-cross(6sqrt(y))+cross(6sqrt(y))-(sqrt(y))^2)

= (24-4sqrt(y)-6sqrt(3)+sqrt(3y))/(36-(sqrt(y))^2)

= (24-4sqrt(y)-6sqrt(3)+sqrt(3y))/(36-y)
}}}

Edwin</pre>