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To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator, which is 3+sqrt(6).

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Here are the solutions to the problems:

1. Express 33−6\frac{3}{3-\sqrt{6}} in the form x+myx+m\sqrt{y}.

  1. To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator, which is 3+63+\sqrt{6}.

    33−6×3+63+6\frac{3}{3-\sqrt{6}} \times \frac{3+\sqrt{6}}{3+\sqrt{6}}
  2. Expand the numerator and denominator.

    Numerator: 3(3+6)=9+363(3+\sqrt{6}) = 9 + 3\sqrt{6}
    Denominator: (3−6)(3+6)(3-\sqrt{6})(3+\sqrt{6}). This is in the form $(a-b)(a+b

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