Final answer:
The expression ((a)/(b)+4)/(2(a)/(b)-5) can be rewritten with the numerator and denominator in rational form as (a + 4b)/(2a - 5b).
Step-by-step explanation:
To rewrite the given expression ((a)/(b)+4)/(2(a)/(b)-5) with the numerator and denominator in rational form, start by evaluating each fraction separately. The expression (a)/(b)+4 can be rewritten as (a + 4b)/b, and 2(a)/(b)-5 can be written as 2a/(b) - 5.
By placing these rewritten fractions as the numerator and denominator, the expression simplifies to (a + 4b)/(2a - 5b). This form ensures that both the numerator and denominator are in rational expression format, allowing for further calculations if needed.
When working with rational expressions, it's crucial to transform the fractions to a common denominator to perform arithmetic operations. By expressing the original given expression with the numerator and denominator both in terms of a single fraction format—(a + 4b)/(2a - 5b)—it becomes easier to manipulate or simplify the expression further if required. This form clarifies the relationship between the terms, allowing for easier analysis or computation of the expression.