To add or subtract rational expressions with common denominators, add or subtract numerators and place the sum or difference over the common denominator.
Finding the Least Common Denominator (LCD):
1. Factor each denominator completely.
2. The least common denominator (LCD) is the product of all unique factors found in Step 1. each raised to a power equal to the greatest number of times that the factor appears in anyone factored denominator.
To add or subtract rational expressions with unlike denominators:
1. Find the LCD of the rational expressions.
2. Rewrite each rational expression as an equivalent expression whose denominator is the LCD found in Step 1.
3. Add or subtract numerators and write the sum or difference over the common denominator.
4. Simplify or write the rational expression in simplest form.
Here are some typical examples:
Finding the Least Common Denominator (LCD):
1. Factor each denominator completely.
2. The least common denominator (LCD) is the product of all unique factors found in Step 1. each raised to a power equal to the greatest number of times that the factor appears in anyone factored denominator.
To add or subtract rational expressions with unlike denominators:
1. Find the LCD of the rational expressions.
2. Rewrite each rational expression as an equivalent expression whose denominator is the LCD found in Step 1.
3. Add or subtract numerators and write the sum or difference over the common denominator.
4. Simplify or write the rational expression in simplest form.
Here are some typical examples: