The image you uploaded contains two fractions, and it seems you are asked to rationalize their denominators.

• A = 3/√6
• B = 5/(√(1) - 2)

Let's proceed to rationalize the denominators for both expressions:

1. For A = 3/√6:

To rationalize the denominator, multiply both the numerator and denominator by √6.

$A = \frac{3}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}} = \frac{3\sqrt{6}}{6}$

2. For B = 5/(√(1) - 2):

This is an expression involving a binomial. To rationalize, multiply the numerator and denominator by the conjugate of the denominator, which is (√(1) + 2).

$B = \frac{5}{\sqrt{1} - 2} \times \frac{\sqrt{1} + 2}{\sqrt{1} + 2} = \frac{5(\sqrt{1} + 2)}{(\sqrt{1})^2 - 2^2}$

Simplifying the denominator:

$(\sqrt{1})^2 - 2^2 = 1 - 4 = -3$

So:

$B = \frac{5(\sqrt{1} + 2)}{-3} = \frac{5(1 + 2)}{-3} = \frac{5 \times 3}{-3} = -5$

Final answers:

• A = 3√6 / 6
• B = -5

Would you like a more detailed breakdown or have any questions about these steps?

Further exploration:

1. How does rationalizing the denominator affect the expression's value?
2. What is the difference between rationalizing a single radical versus a binomial denominator?
3. What happens when you rationalize a fraction with higher powers of radicals?
4. Can you explain the conjugate of a binomial with square roots in more detail?
5. How would you handle fractions with cube roots in the denominator?

Tip: When rationalizing fractions with square roots in the denominator, remember to always multiply by the same radical in both the numerator and denominator to maintain the value of the expression.