Rationalizing the denominator of a fraction involves getting rid of any radicals (square roots, cube roots, etc.) in the denominator. In this case, we need to rationalize the denominator of the fraction 5/6 - √5.

To do this, we can follow these steps:

Step 1: Identify the denominator

The denominator of the given fraction is 6 - √5.

Step 2: Multiply the numerator and denominator by the conjugate of the denominator

The conjugate of a binomial is formed by changing the sign between the terms. In this case, the conjugate of 6 - √5 is 6 + √5.

So, we multiply the numerator and denominator by 6 + √5:

(5/6 - √5) * (6 + √5) / (6 - √5) * (6 + √5)

Step 3: Simplify the expression

Multiplying the numerators and denominators, we get:

(5 * 6 + 5 * √5) / (6 * 6 - √5 * √5)

Simplifying further:

(30 + 5√5) / (36 - 5)

Step 4: Continue simplifying

The denominator can be simplified further:

36 - 5 = 31

So, the expression becomes:

(30 + 5√5) / 31

This is the rationalized form of the given fraction.

Summary:

To rationalize the denominator of the fraction 5/6 - √5, we multiplied the numerator and denominator by the conjugate of the denominator, which is 6 + √5. Simplifying the expression, we obtained (30 + 5√5) / 31 as the rationalized form.