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The conjugate of  a + b  is  a - b  and the conjugate of  a - b  is  a + b.

 

To simplify this problem, multiply both the numerator and the denominator of the fraction by

the conjugate of the denominator:  sqrt(5) + sqrt(2).

 

[ sqrt(5) + sqrt(2) ] / [ sqrt(5) - sqrt(2) ]  · [ sqrt(5) + sqrt(2) ] / [ sqrt(5) + sqrt(2) ]

=

[ sqrt(5) + sqrt(2) ] · [ sqrt(5) + sqrt(2) ]  /  [ sqrt(5) - sqrt(2) · [ sqrt(5) + sqrt(2) ]

=

[ 5 + 2·sqrt(5)·sqrt(2) + 2 ] / [ 5 - 2 ]

=

[ 7 + 2·sqrt(10) ] / 3