33% of the water consumption is industrial use and 21% is personal use so (33% - 21%) = 12% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{12}{100} \) x 30,000 gallons = 3,600 gallons.

To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{32}{60} \) = \( \frac{\frac{32}{4}}{\frac{60}{4}} \) = \( \frac{8}{15} \)

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

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

5 + (3 + 2) ÷ 3 x 4 - 3²
P: 5 + (5) ÷ 3 x 4 - 3²
E: 5 + 5 ÷ 3 x 4 - 9
MD: 5 + \( \frac{5}{3} \) x 4 - 9
MD: 5 + \( \frac{20}{3} \) - 9
AS: \( \frac{15}{3} \) + \( \frac{20}{3} \) - 9
AS: \( \frac{35}{3} \) - 9
AS: \( \frac{35 - 27}{3} \)
\( \frac{8}{3} \)
2\(\frac{2}{3}\)

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)