To divide fractions, invert the second fraction and then multiply:

\( \frac{1}{6} \) ÷ \( \frac{1}{5} \) = \( \frac{1}{6} \) x \( \frac{5}{1} \)

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

\( \frac{1}{6} \) x \( \frac{5}{1} \) = \( \frac{1 x 5}{6 x 1} \) = \( \frac{5}{6} \) = \(\frac{5}{6}\)

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:

\( \frac{-5x^6}{7x^4} \)
\( \frac{-5}{7} \) x^{(6 - 4)}
-\(\frac{5}{7}\)x²

To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 6 factors [1, 2, 4, 7, 14, 28] making 28 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{56} \) = \( \frac{\frac{28}{28}}{\frac{56}{28}} \) = \( \frac{1}{2} \)

The greatest common factor (GCF) is the greatest factor that divides two integers.

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 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.

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

\( \frac{8 x 4}{6 x 4} \) - \( \frac{6 x 3}{8 x 3} \)

\( \frac{32}{24} \) - \( \frac{18}{24} \)

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

\( \frac{32 - 18}{24} \) = \( \frac{14}{24} \) = \(\frac{7}{12}\)