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:

\( \frac{7 x 3}{4 x 3} \) - \( \frac{5 x 1}{12 x 1} \)

\( \frac{21}{12} \) - \( \frac{5}{12} \)

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

\( \frac{21 - 5}{12} \) = \( \frac{16}{12} \) = 1\(\frac{1}{3}\)

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

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

-7y⁴ + 5y⁴
(-7 + 5)y⁴
-2y⁴

The factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 the greatest factor 48 and 68 have in common.