# Calculate. 1\ (x^(1/3)+y^(1/3))

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Cael Cox
$1/\left({x}^{\left(1/3\right)}+{y}^{\left(1/3\right)}\right)$
$=\left({x}^{\left(2/3\right)}+{y}^{\left(2/3\right)}-\left(xy{\right)}^{\left(1/3\right)}\right)/\left(x+y\right)$
ie. multiply and divide by $\left({x}^{\left(2/3\right)}+{y}^{\left(2/3\right)}-\left(xy{\right)}^{\left(1/3\right)}\right)$.
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Nash Frank
I assume you are required to rationalize the denominator.
Use the sum of cubes formula,${x}^{3}+{y}^{3}=\left(x+y\right)\left({x}^{2}-xy+{y}^{2}\right)$
for your question use $x+y=\left({x}^{1/3}+{y}^{1/3}\right)\left({x}^{2/3}-{x}^{1/3}{y}^{1/3}+{y}^{2/3}\right)$
multiply numerator and denominator by $\left({x}^{2/3}-{x}^{1/3}{y}^{1/3}+{y}^{2/3}\right)$
to get $\left({x}^{2/3}-{x}^{1/3}{y}^{1/3}+{y}^{2/3}\right)/\left(x+y\right)$