To add 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:

\( \frac{5 x 3}{4 x 3} \) + \( \frac{9 x 1}{12 x 1} \)

\( \frac{15}{12} \) + \( \frac{9}{12} \)

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

\( \frac{15 + 9}{12} \) = \( \frac{24}{12} \) = 2

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

To fill a 8 gallon tank exactly halfway you'll need 4 gallons of fuel. Each fuel can holds 1 gallons so:

cans = \( \frac{4 \text{ gallons}}{1 \text{ gallons}} \) = 4

The factors of a number are all positive integers that divide evenly into the number. The factors of 32 are 1, 2, 4, 8, 16, 32.

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:

\( \frac{-8x^7}{6x^2} \)
\( \frac{-8}{6} \) x^{(7 - 2)}
-1\(\frac{1}{3}\)x⁵