To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{42\sqrt{12}}{6\sqrt{4}} \)
\( \frac{42}{6} \) \( \sqrt{\frac{12}{4}} \)
7 \( \sqrt{3} \)

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 6 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{6 x 3}{4 x 3} \) + \( \frac{5 x 2}{6 x 2} \)

\( \frac{18}{12} \) + \( \frac{10}{12} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{18 + 10}{12} \) = \( \frac{28}{12} \) = 2\(\frac{1}{3}\)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{9} \) x \( \frac{3}{6} \) = \( \frac{3 x 3}{9 x 6} \) = \( \frac{9}{54} \) = \(\frac{1}{6}\)

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (2 + 3) ÷ 4 x 5 - 4²
P: 4 + (5) ÷ 4 x 5 - 4²
E: 4 + 5 ÷ 4 x 5 - 16
MD: 4 + \( \frac{5}{4} \) x 5 - 16
MD: 4 + \( \frac{25}{4} \) - 16
AS: \( \frac{16}{4} \) + \( \frac{25}{4} \) - 16
AS: \( \frac{41}{4} \) - 16
AS: \( \frac{41 - 64}{4} \)
\( \frac{-23}{4} \)
-5\(\frac{3}{4}\)

A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

33,000 fans x \( \frac{5}{6} \) = \( \frac{165000}{6} \) = 27,500 fans.