is equivalent to multiplying the numerator and denominator of the original

Is equivalent to multiplying the numerator and

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is equivalent to multiplying the numerator and denominator of the original expression by 6. Creating Equivalent Rational Expressions Convert each expression to an equivalent rational expression with the indicated denominator. a. b. w w 5 w 2 3 w 10 7 5 p 2 20 p 6 Example 3 6 6 1 2 6 6 1 2 1 2 1 2 6 6 1 6 2 6 6 12 1 2 p q p q 1 p q r r pr qr r 0, q 0 6 z 7 ; 1 7 z 6 x 2 5 x 6 5 x 2 4 ; 1 2 x 6 ; 1 9 a 3 b 2 ; 5 18 a 4 b 7 40 ; 1 15 ; 5 6 Skill Practice 1 x 3 2 . 1 3 x 2 x 3 3 x 3 x x 3 LCD 1 1 21 3 x 2 LCD 1 x 3 21 1 2 x 4 1 1 x 3 2 ; 1 3 x x 4 x 3 ; 1 1 1 3 x 2 If 1 x 3 and 3 x x 4 x 3 ; 1 3 x 424 Chapter 6 Rational Expressions and Rational Equations Skill Practice Answers 4. 120 5. 6. 2( x 2)( x 2)( x 3) 7. z 7 or 7 z 18 a 4 b 2
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Section 6.3 Addition and Subtraction of Rational Expressions 425 Solution: a. can be written as . Multiply the numerator and denominator by the missing factor, b. Factor the denominator. Multiply the numerator and denominator by the missing factor Fill in the blank to make an equivalent fraction with the given denominator. 8. 9. 5 b b 3 b 2 9 1 8 xy 16 x 3 y 2 Skill Practice w 2 2 w 1 w 5 21 w 2 2 1 w 2 2 . w w 5 w w 5 w 2 w 2 1 w 5 21 w 2 2 w w 5 w 2 3 w 10 28 p 4 20 p 6 4 p 4 . 7 5 p 2 7 5 p 2 4 p 4 4 p 4 5 p 2 4 p 4 20 p 6 5 p 2 4 p 4 7 5 p 2 20 p 6 4. Addition and Subtraction of Rational Expressions with Unlike Denominators To add or subtract rational expressions with unlike denominators, we must con- vert each expression to an equivalent expression with the same denominator. For example, consider adding the expressions . The LCD is For each expression, identify the factors from the LCD that are missing in the denominator. Then multiply the numerator and denominator of the expression by the missing factor(s): The rational expressions now have the same denominator and can be added. 1 3 2 1 x 2 2 1 x 1 2 1 x 1 2 1 5 2 1 x 1 2 1 x 2 2 1 x 2 2 1 x 2 21 x 1 2 . 3 x 2 5 x 1 TIP: In the final answer in Example 3(b) we multiplied the polynomials in the numerator but left the denominator in factored form. This convention is followed because when we add and subtract rational expressions, the terms in the numerators must be combined. Skill Practice Answers 8. 9. 5 b 2 15 b 2 x 2 y
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426 Chapter 6 Rational Expressions and Rational Equations Combine terms in the numerator. Clear parentheses and simplify. 8 x 7 1 x 2 21 x 1 2 3 x 3 5 x 10 1 x 2 21 x 1 2 3 1 x 1 2 5 1 x 2 2 1 x 2 21 x 1 2 Steps to Add or Subtract Rational Expressions 1. Factor the denominator of each rational expression. 2. Identify the LCD. 3. Rewrite each rational expression as an equivalent expression with the LCD as its denominator. 4. Add or subtract the numerators, and write the result over the common denominator. 5. Simplify if possible. Adding and Subtracting Rational Expressions with Unlike Denominators Add or subtract as indicated.
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  • Fractions, Fraction, Elementary arithmetic, Rational function, Greatest common divisor, Subtraction of Rational Expressions

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