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?

Question

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?

Marcel Mccullough · Accepted Answer

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  zWith   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.

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

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