Simplify \(\frac{x – y}{x^{\frac{1}{3}} – y^{\frac{1}{3}}}\)
- x2 + xy + y2
-
x\(\frac{2}{3}\) + x \(\frac{1}{3}\) + y\(\frac{2}{3}\)
- x\(\frac{2}{3}\) - x\(\frac{1}{3}\)y\(\frac{2}{3}\)
- y\(\frac{2}{3}\)
The correct answer is: 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 = (\(x^{\frac{2}{3}}\) + \(x^{\frac{1}{3}}\)\(y^{\frac{1}{3}}\) + \(y^{\frac{2}{3}}\))