To add 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 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.

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

\( \frac{2 x 2}{6 x 2} \) + \( \frac{2 x 1}{12 x 1} \)

\( \frac{4}{12} \) + \( \frac{2}{12} \)

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

\( \frac{4 + 2}{12} \) = \( \frac{6}{12} \) = \(\frac{1}{2}\)

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

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{385mi}{55mph} \)
7 hours

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

2c⁶ - 9c⁶
(2 - 9)c⁶
-7c⁶

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:

\( \frac{6!}{3!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{6 \times 5 \times 4}{1} \)
\( 6 \times 5 \times 4 \)
120

To simplify a radical, factor out the perfect squares:

\( \sqrt{175} \)
\( \sqrt{25 \times 7} \)
\( \sqrt{5^2 \times 7} \)
5\( \sqrt{7} \)