How do I rationalize the following fraction: 1/(9root[3](9)-3root[3](3)-27)?

solvarmedw 2022-10-02 Answered
How do I rationalize the following fraction: 1 9 9 3 3 3 3 27 ?
As the title says I need to rationalize the fraction: 1 9 9 3 3 3 3 27 . I wrote the denominator as: 9 4 3 9 2 3 3 3 but I do not know what to do after. Can you help me?
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Answers (1)

Marcel Mccullough
Answered 2022-10-03 Author has 11 answers
We have
( x + y + z ) ( x 2 + y 2 + z 2 x y x z y z ) = x 3 + y 3 + z 3 3 x y z
With x = 9 9 3 , y = 3 3 3 , z = 27 all terms on the right side are rational, try it. So multiply the given numerator and denominator by x 2 + y 2 + z 2 x y x z y z with x , y , z as rendered above.
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