8.4 Add and Subtract Rational Expressions with Unlike Denominators
2 min read•june 25, 2024
with can be tricky, but they're essential for algebra. You'll learn how to find the and use it to add or subtract fractions. This skill is crucial for solving more complex equations later on.
Don't worry if it seems complicated at first. With practice, you'll get the hang of converting fractions, adding numerators, and simplifying results. These techniques will help you tackle more advanced math problems in the future.
Adding and Subtracting Rational Expressions with Unlike Denominators
Least common denominator for rational expressions
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Find the smallest common multiple of the denominators called the least (LCD)
Determine the of each
LCD is the product of the highest power of each prime factor among all denominators
Example: Find the LCD of 152 and 203
Prime factorization of 15: 3×5
Prime factorization of 20: 22×5
Highest power of 2 is 2, highest power of 3 is 1, and highest power of 5 is 1
LCD = 22×3×5=60
Conversion to common denominators
Multiply the and denominator of each expression by the appropriate factor to convert rational expressions to with a common denominator
Appropriate factor is the LCD divided by the current denominator
Example: Convert 152 and 203 to equivalent forms with the LCD of 60
For 152, multiply numerator and denominator by 1560=4: 152×44=608
For 203, multiply numerator and denominator by 2060=3: 203×33=609
This process involves to ensure the fractions remain equivalent
Addition of unlike rational expressions
Convert rational expressions with different denominators to equivalent forms with a common denominator (the LCD)
Add the numerators and keep the common denominator
Simplify the result if possible by
Example: Add 152+203
Convert to equivalent forms with LCD of 60: 608+609
Add numerators: 608+9=6017
Simplify the result: 6017 cannot be reduced further
Subtraction of unlike rational expressions
Convert rational expressions with different denominators to equivalent forms with a common denominator (the LCD)
Subtract the numerators and keep the common denominator
Simplify the result if possible by reducing the fraction
Example: Subtract 127−185
Convert to equivalent forms with LCD of 36: 3621−3610
Subtract numerators: 3621−10=3611
Simplify the result: 3611 cannot be reduced further
Working with algebraic fractions
are rational expressions with variables in the numerator, denominator, or both
When adding or subtracting algebraic fractions, may be necessary to find the LCD
of the result often involves factoring to cancel common terms
(fractions containing fractions) may require additional steps to simplify before adding or subtracting