Addition and subtraction of algebraic fractions
Addition and Subtraction of Algebraic Fractions
Understanding the Basics
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An algebraic fraction is a fraction where the numerator and/or the denominator are algebraic expressions.
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Algebraic fractions can be added or subtracted just like numerical fractions. However, they have to have a common denominator to simplify or perform additional mathematical operations.
Key Characteristics
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Algebraic fractions often contain variables in the numerator, denominator, or both.
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The primary characteristic of addition and subtraction of algebraic fractions involves applying the principles of rational numbers to algebraic expressions.
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Before conducting addition or subtraction, ensure that the fractions have the same denominator. This is a result of the fundamental rule of fractions that only likewise terms can be directly added or subtracted.
Pointers for Solving these Fractions
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Determine the lowest common denominator (LCD) of the algebraic fractions involved.
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Convert all fractions so they each have the LCD.
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You may then add or subtract the fractions, summing or subtracting the numerators, while the denominator, the LCD, remains the same.
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Finally, simplify the resulting algebraic fraction, if necessary.
Example Illustrations
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To illustrate: if you were to add (2/x) + (3/y), first identify the LCD, which in this case is xy. Rewrite the fractions as (2y/xy) + (3x/xy). The resulting fraction is (2y + 3x)/xy.
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Another example: to subtract (5/a) - (4/b), determine the LCD, which is ab. Rewrite the first fraction as (5b/ab) and the second one as (4a/ab). The resulting fraction is (5b - 4a)/ab.
In Conclusion
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To add or subtract algebraic fractions ensure they have a common denominator.
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To find the common denominator, you may have to multiply or manipulate the original fractions.
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It’s crucial to be proficient with these operations as they form the core of handling and solving more complex algebraic expressions. Remember to simplify your final answer.