SOLUTION: Rationalize the denominators {{{ sqrt( 7 ) - sqrt( 6 )}}} / {{{ sqrt( 7 ) + sqrt( 6 )}}} Combine {{{ 8sqrt( 12 ) - 3sqrt( 27 ) }}}

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To rationalize a denominator that is the sum or difference of two square roots, you need to recall the factorization of the difference of two squares, namely:



If you multiply the denominator of your fraction by , you will get for your new denominator. But in order to introduce that factor into the denominator, you have to multiply the entire fraction by 1 in the form of .

Here is the entire expression: .

Now, multiply the binomials and simplify: