+49 Simplify the expression
\[\frac{1}{\sqrt{36} + \sqrt{27}} + \frac{1}{\sqrt{27} + \sqrt{18}} + \frac{1}{\sqrt{18} + \sqrt{9}}.\]
+23252 1 / [ sqrt(36) + sqrt(27) ] = 1 / [ 6 + 3sqrt(3) ] = 1 / [ 3·( 2 + sqrt(3) ) ]
1 / [ sqrt(27) + sqrt(18) ] = 1 / [ 3sqrt(3) + 3sqrt(2) ] = 1 / [ 3·( sqrt(3) + sqrt(2) ) ]
1 / [ sqrt(18) + sqrt(9) ] = 1 / [ 3sqrt(2) + 3 ] = 1 / [ 3·( sqrt(2) + 1 ) ]
So, the common denominator is: 3 · ( 2 + sqrt(3) ) · ( sqrt(3) + sqrt(2) ) ·( sqrt(2) + 1 ) ]
Multiply the numerator and denominator of the first term by: ( sqrt(3) + sqrt(2) ) ·( sqrt(2) + 1 )
Multiply the numerator and denominator of the second term by: ( 2 + sqrt(3) ) · ( sqrt(2) + 1 )
Multiply the numerator and denominator of the third term by: ( 2 + sqrt(3) ) · ( sqrt(3) + sqrt(2) )
This will be messy; if you need further help -- ask ...
