As an expert in the field of mathematics, I'm pleased to guide you through the process of adding and subtracting rational numbers with unlike denominators. This is a fundamental skill in algebra that is essential for understanding more complex mathematical concepts.

When dealing with rational numbers, or fractions, that have different denominators, the process involves several steps to ensure that you are working with like terms, which is a prerequisite for addition and subtraction. Here's how you can do it:


1. Identify the Denominators: The first step is to identify the denominators of the fractions you are working with. These are the numbers at the bottom of the fractions.


2. Find the Least Common Multiple (LCM): The next step is to find the Least Common Multiple of these denominators. The LCM is the smallest number that all the denominators can divide into without leaving a remainder. This is crucial because it will serve as the common denominator for all the fractions involved.


3. Convert to Equivalent Fractions: Once you have the LCM, you need to convert each fraction to an equivalent fraction that has the LCM as its denominator. This involves multiplying both the numerator and the denominator of each fraction by the appropriate factor to achieve the LCM.

4. **Write Each Expression Using the LCD (Least Common Denominator)**: After converting the fractions, you will rewrite each expression using the LCM as the common denominator. This is referred to as the LCD.


5. Add or Subtract the Numerators: With the fractions now having the same denominator, you can proceed to add or subtract the numerators directly. Remember, the denominator remains unchanged.


6. Simplify as Needed: After performing the addition or subtraction, you may end up with a fraction that can be simplified. Look for factors that the numerator and denominator have in common and divide both by these factors to reduce the fraction to its simplest form.

This process ensures that you are working with like terms and allows you to accurately perform the operations of addition and subtraction on fractions with unlike denominators.

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There are a few steps to follow when you add or subtract rational expressions with unlike denominators.To add or subtract rational expressions with unlike denominators, first find the LCM of the denominator. ... Write each expression using the LCD. ... Add or subtract the numerators.Simplify as needed.read more >>