Final answer:
The least common denominator (LCD) for the fractions (5/3) and (3/7x) is 21x. The equivalent fractions with this LCD are (35x/21x) and (9/21x).
Step-by-step explanation:
The student has asked us to find the least common denominator (LCD) and the list the rational expression obtained from the given expressions (5/3) and (3/7x).
To find the LCD, you need to find the smallest number that both denominators can divide into without leaving a remainder. The denominators in the given expressions are 3 and 7x. Since these denominators have no common factors (other than 1) and are not multiples of each other, the LCD is simply their product, which is 21x.
Next, we'll convert each fraction to an equivalent fraction with the LCD as the new denominator:
- For (5/3), we multiply both the numerator and denominator by 7x to get (35x/21x).
- For (3/7x), we multiply both the numerator and denominator by 3 to get (9/21x).
Thus, the list of rational expressions with the LCD as the denominator is (35x/21x) and (9/21x).