91Ó°ÊÓ

When dealing with algebraic fractions, identifying a common denominator is a crucial first step. A denominator is the bottom part of a fraction, and when we try to add or subtract fractions, they must have the same denominator to proceed. For example, in the original exercise \( \frac{4}{5h} - \frac{k}{5h} \), both fractions already have \( 5h \) as their common denominator. This allows us to move directly to the next steps without the need to find or convert denominators. Understanding common denominators helps streamline the process of working with fractions, especially when they contain variables. By ensuring the denominators match, we align the fractions onto a common playing field for further operations.

Once a common denominator is established, the next focal point is the numerators—the top parts of the fractions. In subtraction of fractions, we are concerned only with the numerators, since the denominators remain fixed once they are common. Take the algebraic fractions in the example: \( \frac{4}{5h} - \frac{k}{5h} \). Since the denominators match (\( 5h \)), we can simply subtract the second numerator from the first:

• Start with the initial numerator, \( 4 \).
• Subtract the second numerator, \( k \), from it.

This gives us \( 4 - k \) as the new numerator. This process simplifies our expression by combining the effects of the numerators while keeping the once common denominator intact.

The final step in working with algebraic fractions is simplifying the expression. Even when the fraction is not numerical, the goal remains the same: make it as straightforward as possible. In the given task, after successfully subtracting the numerators (i.e., finding \( 4 - k \)), we are left with \( \frac{4-k}{5h} \). At this point, simplifying refers to ensuring there are no further alterations we can make to break down the fraction more. Sometimes simplification involves canceling common factors between the numerator and denominator or factoring algebraic terms. However, since the terms \( 4-k \) and \( 5h \) share no common factors here, the expression is already in its simplest form. By simplifying, we ensure that anyone who looks at the fraction sees only the necessary parts and none of the excess that complicates understanding the expression.