To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.

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

\( \frac{9 x 7}{6 x 7} \) - \( \frac{9 x 3}{14 x 3} \)

\( \frac{63}{42} \) - \( \frac{27}{42} \)

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

\( \frac{63 - 27}{42} \) = \( \frac{36}{42} \) = \(\frac{6}{7}\)

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

9\( \sqrt{5} \) x 3\( \sqrt{9} \)
(9 x 3)\( \sqrt{5 \times 9} \)
27\( \sqrt{45} \)

Now we need to simplify the radical:

27\( \sqrt{45} \)
27\( \sqrt{5 \times 9} \)
27\( \sqrt{5 \times 3^2} \)
(27)(3)\( \sqrt{5} \)
81\( \sqrt{5} \)

62% of the water consumption is industrial use and 27% is personal use so (62% - 27%) = 35% more water is used for industrial purposes. 25,000 gallons are consumed daily so industry consumes \( \frac{35}{100} \) x 25,000 gallons = 8,750 gallons.

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{9a^8}{2a^3} \)
\( \frac{9}{2} \) a^{(8 - 3)}
4\(\frac{1}{2}\)a⁵

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 60mph \times 5h \)
300 miles