91Ó°ÊÓ

When you add or subtract rational expressions, finding the common denominator is crucial. The denominator is the bottom part of a fraction. For two fractions to be added or subtracted, their denominators need to be the same. In the given exercise, the fractions \(\frac{5}{r}\) and \(\frac{9}{r}\) already share the denominator \(\r\). This makes our job easier because we don't need to modify the fractions to have a common denominator.
Remember, if the denominators were different, you would need to find the least common multiple (LCM) of the denominators before you'd add the numerators.
In cases where the denominators are not the same, finding the LCM ensures that both fractions are adjusted to have a uniform bottom part, making addition or subtraction feasible.

Simplifying fractions means expressing the fraction in its simplest form. In the provided exercise, the final result is \(\frac{14}{r}\), which is already in its simplest form because 14 and r have no common factors other than 1.
Here are some tips for simplifying fractions:

• Check if the numerator and the denominator have any common factors apart from 1.
• Divide both the numerator and the denominator by their greatest common divisor (GCD).
• Repeat the process until you can’t simplify anymore.

The goal is to make the fraction as simple as possible while keeping its value the same.
Simplification helps in making calculations easier and also gives a clearer understanding of the values involved.

In any fraction, the numerator and denominator play essential roles. The numerator is the top part of the fraction, indicating how many parts you have. The denominator is the bottom part, showing into how many parts the whole is divided.
For example, in the fraction \(\frac{5}{r}\), 5 is the numerator and \(r\) is the denominator.
When adding fractions like \(\frac{5}{r}\) and \(\frac{9}{r}\), you focus on the numerators \(5\) and \(9\). You keep the denominator \(r\) the same and add the numerators: \(\frac{5+9}{r} = \frac{14}{r}\).
Understanding the roles of numerators and denominators will help you perform operations on fractions correctly and avoid common mistakes.
Always remember:

• The numerator tells you how many parts.
• The denominator tells you the size of each part.

This fundamental understanding is key to mastering rational expressions and fractions.