Final answer:
To simplify the expression, first convert the mixed numbers to improper fractions. Then, divide the second mixed number by the third mixed number. Simplify the resulting expression by combining like terms.
Step-by-step explanation:
First, we need to simplify the expression. Start by simplifying the mixed numbers:
2 1/4x = 9/4x
4 1/3x = 13/3x
7 4/5 = 39/5
Next, divide the second mixed number by the third mixed number:
(13/3x - 39/5) ÷ 2 3/5
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(13/3x - 39/5) × (5/13) = (65/39x - 39/1)
Now, we can simplify the expression further:
9/4x + (65/39x - 39/1)
To add or subtract fractions with the same denominator, we add or subtract the numerators:
(9/4x + 65/39x) - (39/1) = (9/4x + 65/39x - 39)
Finally, we simplify the fractions:
(9/4x + 65/39x - 39) = (877/156x - 39)