Question 375384
Please help me simplify this {{{ (x^(1/3)-1)/(x-1) }}}
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You can treat the denominator as a difference of 2 cubes with 
{{{x = (x^(1/3))^3}}}
Sub y for x^1/3
{{{ (x^(1/3)-1)/(x-1) = (y - 1)/(y^3 - 1)}}}
= {{{(y-1)/((y-1)*(y^2 + y + 1))}}}
= {{{1/(y^2 + y + 1))}}}
Sub back for y
= {{{1/(x^(2/3) + x^(1/3) + 1)}}}
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Do you consider that simpler?  I don't.
I would answer that the original cannot be simplified.