Final answer:
The expression (9)/(4x) - (8)/(5x) is simplified by finding a common denominator which is 20x, leading to the reduced form (13)/(20x).
Step-by-step explanation:
The student is asking how to express the algebraic expression (9)/(4x) - (8)/(5x) in its fully reduced form. This is a mathematics problem that involves simplifying expressions with variables.
To combine these fractions, we need a common denominator. First, we find the least common multiple (LCM) of the two denominators, which is 20x. We then adjust each fraction to have this LCM as its new denominator by multiplying both the numerator and the denominator of each fraction by the appropriate factor. For the first fraction, we multiply the numerator and denominator by 5, and for the second fraction, we multiply by 4:
- (9)/(4x) * (5)/(5) = (45)/(20x)
- (8)/(5x) * (4)/(4) = (32)/(20x)
Now, we can subtract the second expression from the first:
(45)/(20x) - (32)/(20x) = (45 - 32)/(20x) = (13)/(20x)
The resulting expression is (13)/(20x), which is already in its reduced form, as the numerator and denominator have no common factors other than 1. Therefore, we cannot reduce this fraction any further.