divide the sum of 65/12and12/7by their difference.
come on, guy -- do the math
(65/12 + 12/7)
-------------------- = ?
(65/12 - 12/7)
To divide the sum of two fractions by their difference, you first need to find the sum and difference of the fractions. Let's break down the steps:
Step 1: Find the sum of the fractions.
To find the sum of 65/12 and 12/7, you need to find a common denominator. The least common multiple (LCM) of 12 and 7 is 84, so we can rewrite the fractions with 84 as the common denominator:
65/12 = (65 * 7) / (12 * 7) = 455/84
12/7 = (12 * 12) / (7 * 12) = 144/84
Now, you can add the fractions together:
455/84 + 144/84 = (455 + 144) / 84 = 599/84
Step 2: Find the difference of the fractions.
To find the difference between 65/12 and 12/7, we once again need to use the common denominator of 84:
65/12 = (65 * 7) / (12 * 7) = 455/84
12/7 = (12 * 12) / (7 * 12) = 144/84
Now, subtract the fractions:
455/84 - 144/84 = (455 - 144) / 84 = 311/84
Step 3: Divide the sum by the difference.
To divide the sum by the difference, divide the numerator of the sum by the numerator of the difference, and divide the denominator of the sum by the denominator of the difference:
(599/84) / (311/84) = (599/84) * (84/311) = (599 * 84) / (84 * 311)
Simplifying this expression further requires cancelling any common factors between the numerator and denominator. Let's determine if there are any common factors:
Factors of 599: 1, 13, 23, 599
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 311: 1, 311
Since there are no common factors between the numerator and denominator, you cannot simplify the expression any further.
Therefore, the result of dividing the sum of 65/12 and 12/7 by their difference is:
(599 * 84) / (84 * 311) = 498516 / 25824, and it cannot be simplified further.