- Addition and subtraction of rational expressions can only be performed if they have common denominators.
- If the two rational expressions to be added don't have a common denominator, we need to modify the rational expressions so that equivalent rational expressions have the same denominators.
Adding & Subtracting Rational Expressions
For simplicity's sake, we classify rational expressions' addition and subtraction into two cases.
1. When rational expressions have a common (same) denominator:
- Keep the denominator as it is, and add or subtract the numerators.
- Simplify (cancel out common factors) the remaining expression if possible.
2. When rational expressions have different denominators:
- Find the LCM (least common multiple) of all the denominators.
- Modify the rational expression into an equivalent rational expression with the same denominator (as we do while adding or subtracting fractions with unlike denominators).
- Simplify the resulting rational expression if possible.
Example 1: Add and .
Solution: Here, we see that the denominators of the rational expressions to be added are the same. Hence, we can directly add the numerator terms.
Example 2: Subtract from .
Solution: In this problem, the denominators of the rational expressions to be subtracted are the same. Hence, we can directly perform subtraction operations.
Example 3: Simplify .
Example 4: Simplify .
Example 5: Simplify
- To add or subtract rational expressions, they must have common denominators.
- If the denominators of rational expressions to be added are different, then we must first express them into an equivalent rational expression with common denominators.
- Subtracting from means .
- Abhishek Tiwari
- 10 Comments
- 57 Likes