Question 108255
simplify

[(sqrt 5) - (sqrt 3)] / [3(sqrt 5) + 4(sqrt 3)] 
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Multiply numerator and denominator by [3sqrt5 - 4sqrt3]
to get:

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[(sqrt 5) - (sqrt 3)][3sqrt5 - 4sqrt3] / [3(sqrt 5) + 4(sqrt 3)][3sqrt5 - 4sqrt3] 

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[3*5+4*3-7sqrt(15)] / [9*5-16*3]
= [27 - 7sqrt(15)]/1
= [27 - 7sqrt(15)]
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Cheers,
Stan H.