Correct Answer: Option B

Explanation

\(\frac{x - y}{x^{\frac{1}{3}} - y^{\frac{1}{3}}}\)

( x - y ) = (\(x^{\frac{1}{3}})^3 - (y^{\frac{1}{3}})^3\) = (\(x^{\frac{1}{3}}\) - \(y^{\frac{1}{3}}\))(\(x^{\frac{2}{3}}\) + \(x^{\frac{1}{3}}\)\(y^{\frac{1}{3}}\) + \(y^{\frac{2}{3}}\))

SO, \(\frac{x - y}{x^{\frac{1}{3}} - y^{\frac{1}{3}}}\) = \(\frac{(x^{\frac{1}{3}} - y^{\frac{1}{3}})(x^{\frac{2}{3}} + x^{\frac{1}{3}}y^{\frac{1}{3}} + y^{\frac{2}{3}})}{x^{\frac{1}{3}} - y^{\frac{1}{3}}}\)

Common factor in numerator and denominator cancels out.

Final answer = (\(x^{\frac{2}{3}}\) + \(x^{\frac{1}{3}}\)\(y^{\frac{1}{3}}\) + \(y^{\frac{2}{3}}\))

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