Question 748277
When solving a problem like this, you need to multiply the top and bottom of the fraction by the conjugate of the denominator.

The conjugate is obtained by simply changing the sign between the two terms of the denominator.

{{{(sqrt(8)-sqrt(27))/(sqrt(6)-sqrt(5))}}}


{{{(sqrt(8)-sqrt(27))/(sqrt(6)-sqrt(5))*(sqrt(6)+sqrt(5))/(sqrt(6)+sqrt(5))}}}

Now the bottom will be rationalized:

{{{(sqrt(48)+sqrt(40)-sqrt(162)-sqrt(135))/(6-5)}}}


{{{(sqrt(48)+sqrt(40)-sqrt(162)-sqrt(135))/1}}}

You can simplify the radicals a bit on top if you'd like, but it won't look much prettier.  That's it for rationalizing the denominator.