To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator, which is 3+sqrt(6).
This languages problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
Here are the solutions to the problems:
1. Express $\frac{3}{3-\sqrt{6}}$ in the form $x+m\sqrt{y}$.
Step 1: To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator, which is $3+\sqrt{6}$.
$$ \frac{3}{3-\sqrt{6}} \times \frac{3+\sqrt{6}}{3+\sqrt{6}} $$
Step 2: Expand the numerator and denominator.
Numerator: $3(3+\sqrt{6}) = 9 + 3\sqrt{6}$
Denominator: $(3-\sqrt{6})(3+\sqrt{6})$. This is in the form $(a-b)(a+b
