解：原式=(√5²+2×√5×3+3²)/2²+[2/(√5+3)]²
=[(5+6√5+9)/4]+2²/[(√5²+2×√5×3+3²)]
=(14+6√5)/4+[4/(14+6√5)]
=[(7+3√5)/2]+2/(7+3√5)
=[(7+3√5)/2]+[2(7-3√5)]/[(7+3√5)(7-3√5)]
=[(7+3√5)/2]+[2(7-3√5)]/([7²-(3√5)²]
=[(7+3√5)/2]+[2(7-3√5)]/(49-45)
=[(7+3√5)/2]+[2(7-3√5)]/4
=[(7+3√5)/2]+(7-3√5)/2
=(7+3√5+7-3√5)/2
=14/2
=7
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