Combining Rational Expressions with Unlike Denominators
Combine rational expressions with unlike denominators in Grade 9 algebra. Find the LCD, build equivalent fractions, add or subtract numerators, and simplify the resulting expression.
Key Concepts
New Concept A least common denominator (LCD) is the least common multiple (LCM) of the denominators. What’s next Next, you’ll apply this principle to add and subtract rational expressions by finding the LCD and creating equivalent fractions.
Common Questions
How do you add rational expressions with unlike denominators?
Find the LCD of the denominators, rewrite each fraction with the LCD, add the numerators while keeping the LCD, then simplify or factor the result.
How do you find the LCD of algebraic expressions?
Factor each denominator completely. Take each unique factor at its highest power and multiply them together to form the LCD.
What are common mistakes when combining rational expressions?
Common errors: adding denominators instead of finding LCD, forgetting to distribute when rewriting fractions with LCD, and not factoring to check if results can simplify further.