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When adding fractions, having a common denominator is crucial. The denominator is the bottom part of a fraction. It shows how many equal parts the whole is divided into. For example, in the fraction \( \frac{3}{4} \), the denominator is 4. When two fractions share the same denominator, they have the same 'size' parts.- To find a common denominator, determine the least common multiple of the denominators you are working with. However, if the given fractions already have the same denominator, as in this exercise, the process is simpler.- Just add or subtract the numerators directly, keeping the single shared denominator.For example, with the exercise given, both fractions share the common denominator \( x^{2}+3x \). This means we can proceed to the next step without any further adjustment.

Simplifying fractions is the process of reducing them to their simplest form. This makes them easier to understand and use. A fraction is in its simplest form when the numerator and the denominator have no common factors other than 1.- To simplify, divide both the numerator and the denominator by their greatest common factor (GCF).- In the exercise provided, the expression \( \frac{2x^{2}-x}{x^{2}+3x} \) shows a simplified numerator, obtained from combining like terms.Remember, always check if there's a common factor before concluding that a fraction is fully simplified. In algebra, factoring can further reduce expressions to their simplest form.

The numerator is the top part of a fraction. It tells you how many parts are being considered. For instance, in the fraction \( \frac{3}{4} \), the numerator is 3, meaning three parts out of four.When the fractions have a common denominator, add or subtract the numerators directly:- Combine them as if they were regular numbers, keeping the common denominator.- For instance, in the expression given, the numerators \( x^{2}-2x \) and \( x^{2}+x \) are added to become \( 2x^{2}-x \).Properly managing numerators is essential for correctly solving fraction operations. Always ensure that after addition or subtraction, the result should be as simple as possible. This generally leads to better clarity in your final answer.