To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 share.

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

\( \frac{2 x 7}{5 x 7} \) - \( \frac{6 x 5}{7 x 5} \)

\( \frac{14}{35} \) - \( \frac{30}{35} \)

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

\( \frac{14 - 30}{35} \) = \( \frac{-16}{35} \) = -\(\frac{16}{35}\)

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:

4x⁴ - 3x⁴
(4 - 3)x⁴
x⁴

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

To subtract these radicals together their radicands must be the same:

7\( \sqrt{45} \) - 3\( \sqrt{5} \)
7\( \sqrt{9 \times 5} \) - 3\( \sqrt{5} \)
7\( \sqrt{3^2 \times 5} \) - 3\( \sqrt{5} \)
(7)(3)\( \sqrt{5} \) - 3\( \sqrt{5} \)
21\( \sqrt{5} \) - 3\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them:

The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 have in common.