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5.5 Notes_Adding and Subtracting Rational Expressions.notebook February 26, 2014
Dec 13:35 PM
5.5 Adding and Subtracting Rational Expressions
Add and subtract rational expressions with like denominators• Determine the Lowest Common Multiple• Write equivalent rational expressions using the LCM as the new denominator• Add and subtract rational expressions with unlike denominators
Dec 13:35 PM
How to Add or Subtract Rational Expressions with Like Denominators
1. Add (or subtract) the numerators.2. Keep the common denominator.3. Simplify the result.
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x + 5 3x + 3 2x + 52x2 + 5x + 3 2x2 + 5x + 3 2x2 + 5x + 3
Ex 1:
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5a 30a2 36 36 a2
Ex 2:
Dec 13:35 PM
• Find the LCM of the numbers
• List any variable that occurs ANYWHERE in ANY denominator
• Give each variable the BIGGEST exponent
Finding Least Common Denominators: Monomials
Dec 13:35 PM
Ex 3: Find the LCM
5.5 Notes_Adding and Subtracting Rational Expressions.notebook February 26, 2014
Dec 13:35 PM
4a2b 10ab3
Ex 4: Find the LCM
Dec 13:35 PM
Making Equivalent Expressions• Rewrite numerators
• Make new denominators using LCD
• Determine what you have to multiply each old denominator by to give you the LCD. Multiply the numerator by this.
• Write the new expressions
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+Ex 5: Simplify:
Feb 262:03 PM
Dec 13:35 PM
5 34a2b 10ab3
Ex 6: Simplify:
Dec 13:35 PM
5 12c 6c
+Ex 7: Simplify:
5.5 Notes_Adding and Subtracting Rational Expressions.notebook February 26, 2014
Dec 13:35 PM
Determining the LCD of Polynomials
• Factor all polynomials
• LCD is a product of all the factors that appear in at least one of the polynomials.
• For each factor, use the largest exponent that appears
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Ex 8: Find the LCD
x 7, 4x 28, 6x
Dec 13:35 PM
4 53 x
• LCD?• What will it take to get each denominator equal to the LCD?• Multiply the numerator and denominator by this.• Perform operation indicated.• Simplify if possible.
Ex 9: Simplify:
Dec 13:35 PM
x + 2 4x 3+Ex 10: Simplify:
Dec 13:35 PM
3 2a2 36 6a+Ex 11: Simplify:
Dec 13:35 PM
3x 5x x9x + 2 2 9x 81x2 4
Ex 12: Simplify:
5.5 Notes_Adding and Subtracting Rational Expressions.notebook February 26, 2014
Dec 13:35 PM
x 3x2 + 4x + 3 x2 4x 5
13. Perform the Indicated Operation:
Feb 262:34 PM
Feb 262:41 PM Dec 13:35 PM
14. Perform the Indicated Operation
45x + 89x 2
Dec 13:35 PM
x + 2 33(x + 4) 3(x + 4)
15. Perform the Indicated Operation
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7(x 3y) 2(x + 3y)(x + 3y)2(x 3y) (x 3y)(x + 3y)2
16. Perform the Indicated Operation