A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

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:

\( \frac{6!}{4!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{6 \times 5}{1} \)
\( 6 \times 5 \)
30

The equation for this sequence is:

a_n = a_n-1 + 4(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

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

4 + (2 + 5) ÷ 4 x 3 - 3²
P: 4 + (7) ÷ 4 x 3 - 3²
E: 4 + 7 ÷ 4 x 3 - 9
MD: 4 + \( \frac{7}{4} \) x 3 - 9
MD: 4 + \( \frac{21}{4} \) - 9
AS: \( \frac{16}{4} \) + \( \frac{21}{4} \) - 9
AS: \( \frac{37}{4} \) - 9
AS: \( \frac{37 - 36}{4} \)
\( \frac{1}{4} \)
\(\frac{1}{4}\)

To subtract 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 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 4 and 12 share.

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

\( \frac{8 x 3}{4 x 3} \) - \( \frac{2 x 1}{12 x 1} \)

\( \frac{24}{12} \) - \( \frac{2}{12} \)

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

\( \frac{24 - 2}{12} \) = \( \frac{22}{12} \) = 1\(\frac{5}{6}\)