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Mastering Addition and Subtraction of Rational Expressions

This educational guide focuses on adding and subtracting rational expressions, specifically targeting common factors and simplification techniques. It covers key concepts such as dividing out common factors, finding the least common denominator (LCD), and provides examples for practical understanding. The text emphasizes simplifying rational expressions to their simplest form through factoring, combining like terms, and managing different denominators in operations. Ideal for students seeking to improve their skills in algebra and rational expressions.

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Mastering Addition and Subtraction of Rational Expressions

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  1. 3.5 Adding and Subtracting Rational Expressions 12/12/12

  2. 3 5 x • • Divide out the common factor 5 and simplify. 3x = = 5 x 5 + b. x 6x 2 3 x 3 • • c. Divide out the common factors 2 and x. = = 14x2 2 7 x x 7x • • • Example 1 Simplify a Rational Expression Simplify the rational expression, if possible. 15x a. 5 This expression is already in simplest form.

  3. Ex 1: Simplify = Factor out 3xy

  4. Ex 2: Simplify = Factor out (x+5) = Combine Like Terms

  5. Ex 3: Simplify Big X = Factor out () Simplify brackets = a2 – b2

  6. Different Denominators: When adding/subtracting fractions and the denominators are different, find the least common denominator (LCD).

  7. Ex 4: Simplify LCD:

  8. Ex 5: Simplify Big X LCD: ( Simplify numerator

  9. Ex 6: Simplify Big X LCD: ( Switch the signs of the second numerator Combine Like terms

  10. Homework: WS 3.5 odd only

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