Rational expressions are algebraic fractions where both numerator and denominator are polynomials. This guide explores the addition and subtraction of these expressions, emphasizing the importance of finding a common denominator for those with unlike denominators and simplifying the result. Techniques for combining expressions with identical and distinct denominators are discussed, providing a systematic approach to algebraic manipulation.
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Rational expressions are algebraic expressions with polynomial numerators and denominators
Rational expressions follow the same principles as arithmetic fractions
Understanding rational expressions is crucial for solving algebraic equations involving fractions
When adding or subtracting rational expressions with identical denominators, the numerators are combined while the denominator remains unchanged
After combining like denominators, further simplification may be possible by factoring and canceling like terms
The sum of 2x/35 + 9x/35 can be simplified to 11x/35
The LCD is the least common multiple of the polynomial denominators and is necessary for combining expressions with different denominators
To add or subtract rational expressions with unlike denominators, the denominators are first standardized using the LCD, then the numerators are combined and the expression is simplified
(m+n)/2 + (2n+1)/5 can be simplified to (5m + 7n + 2)/10 by finding the LCD of 2 and 5. (3a + 1)/(4a - 6) + (5a^2)/(2a^2 - 3a) can be simplified further after standardizing the denominators using the LCD of (4a - 6)(2a^2 - 3a)
Proficiency in adding, subtracting, and simplifying rational expressions is essential for solving algebraic equations involving fractions
Rational expressions can be used to model and solve real-world problems, making them an important concept in algebra
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In algebra, expressions similar to fractions but containing ______ are known as rational expressions.
variables
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Combining rational expressions with same denominators
Add or subtract numerators; keep common denominator unchanged.
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Handling different denominators in rational expressions
Find common denominator before combining; adjust numerators accordingly.
