Final answer:
The least common denominator for the fractions 17/5x² and 4/25x is 25x², obtained by finding the LCM of the numerical coefficients and the highest power of the variables present in the denominators.
Step-by-step explanation:
To find the least common denominator (LCD) for the fractions 17/5x² and 4/25x, we need to identify the smallest expression that both denominators can divide into without leaving a remainder. The denominators are 5x² and 25x. First, we find the least common multiple (LCM) of the numerical coefficients, which is the LCM of 5 and 25, equalling 25. Next, we look at the variable parts, where x² and x are present, and choose the highest power of x as part of our LCD, which is x².
Therefore, the least common denominator for the given fractions is 25x². To use these fractions together in addition, subtraction, or comparison, each fraction should be converted to have this common denominator.