Addition and subtraction of rational expression

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1. Addition and Subtraction of Rational Expression Subtitle

2. Let’s Prepare 1. + = = = 2. - = = -1  

3. Rational Expressions with Like Denominators To add or subtract fractions with like denominators simply add or subtract the numerators. Then write the sum or difference over the common denominator. Example 1. + = Since the denominators are the same, that is, both x + 2, simply add the numerators. = + = =  

4. Example 2. + = = Example 3. + = = = Example 4. - = = = = = - Example 5. + = =  

5. Adding and subtracting with like denominators for all rational numbers, we have + = and - = .  

6. Rational Expressions with Unlike Denominators There are instances when rational expressions do not have the same or like denominators. In these cases, we must first find the least common denominator (LCD) of the rational expressions given. LCD is not always recognized, especially in algebraic rational expressions. It must contain all prime factors of each denominator raised to the highest power. It is the common multiple of the denominators. So, in adding or subtracting rational expressions with unlike denominators, find first the LCD or the common multiple of the denominators.

7. Example 1. - Find the LCD, which is 24. Solution: - = - = = Example 2. + Solution: + = + = = =  

8. Example 3. - Find the LCD: 3y = 3 . y 5y = 5 . y LCD = y . 3 . 5 = 15y Solution: - = - = - = - = =  

9. Example 4. - Find the LCD: 9x = 3 . 3 . x 3x 2 = 1 . 3 . x . x LCD = 3x . 3 . 1 . x = 9x 2 So the LCD is 9x 2 = - = - = - = or  

10. When adding or subtracting fractions with unlike denominators, find first the least common denominators (LCD). To generalize, we have + = Addition - = Subtraction  

11. Thank You