Rationalize 1/∛x+∛y

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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Use multiplication by conjugate. This multiplication helps you to remove radicals from denominator.

Use formula: a+b = (`root(3)(a)` + `root(3)b` )`(root(3)(a^2)-root(3)(a*b)+root(3)(b^2))`

Since you have `root(3)x+root(3)y` , the conjugate is `(root(3)(x^2) - root(3)(x*y) + root(3)(y^2))`

Multiply by conjugate =>

=>`1/(root(3)x + root(3)y) = (root(3)(x^2) - root(3)(x*y) + root(3)(y^2))/(x+y)`

ANSWER: The rationalized fraction: `(root(3)(x^2) - root(3)(x*y) + root(3)(y^2))/(x+y).`

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