4
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. Dec 13:35 PM x+5 3x + 3 2x + 5 2x 2 + 5x + 3 2x 2 + 5x + 3 2x 2 + 5x + 3 Ex 1: Dec 13:35 PM 5a 30 a 2 36 36 a 2 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 · 5.5 Notes_Adding and Subtracting Rational Expressions.notebook February 26, 2014 Dec 13:35 PM Determining the LCD

  • Upload
    others

  • View
    2

  • Download
    0

Embed Size (px)

Citation preview

Page 1: 5.5 Notes Adding and Subtracting Rational Expressions.notebook · 5.5 Notes_Adding and Subtracting Rational Expressions.notebook February 26, 2014 Dec 13:35 PM Determining the LCD

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.

Dec 1­3:35 PM

    x + 5      3x + 3       2x + 52x2 + 5x + 3     2x2 + 5x + 3 2x2 + 5x + 3

Ex 1:

Dec 1­3:35 PM

  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

Page 2: 5.5 Notes Adding and Subtracting Rational Expressions.notebook · 5.5 Notes_Adding and Subtracting Rational Expressions.notebook February 26, 2014 Dec 13:35 PM Determining the LCD

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

Dec 1­3:35 PM

+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:

Page 3: 5.5 Notes Adding and Subtracting Rational Expressions.notebook · 5.5 Notes_Adding and Subtracting Rational Expressions.notebook February 26, 2014 Dec 13:35 PM Determining the LCD

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

Dec 1­3:35 PM

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:

Page 4: 5.5 Notes Adding and Subtracting Rational Expressions.notebook · 5.5 Notes_Adding and Subtracting Rational Expressions.notebook February 26, 2014 Dec 13:35 PM Determining the LCD

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

Dec 1­3:35 PM

    7(x ­ 3y)        2(x + 3y)(x + 3y)2(x ­ 3y)    (x ­ 3y)(x + 3y)2

16.  Perform the Indicated Operation