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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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For more information, please see full course syllabus of Algebra 1
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Lecture Comments (3)

2 answers

Last reply by: Michael Romanov
Tue Nov 29, 2016 9:48 AM

Post by EN N on March 10 at 02:46:14 PM

in example 2 can't - 4z+1 over 4z+1 be reduced to - 1 over 1

Adding and Subtracting Rational Expressions with Like Denominators

  • To add or subtract fractions with like denominators, add or subtract the numerators. Then simplify the result.
  • Most of the time, the result will not simplify, but always check to see if the numerator and denominator have any common factors.
  • Sometimes, instead of being equal, the two binomial denominators are additive inverses of each other. In such a situation, factor –1 out of either denominator to make the two denominators equal to each other. Then carry out the addition or subtraction as above. Be sure to include the factor of –1 as you are doing this.

Adding and Subtracting Rational Expressions with Like Denominators

[13/3c] + [8/3c]
  • [(13 + 8)/3c]
  • [21/3c]
[7/c]
[22/6t] + [10/6t]
  • [(22 + 10)/6t]
  • [32/6t]
[16/3t]
[15/2q] − [9/2q]
  • [(15 − 9)/2q]
  • [6/2q]
[3/q]
[(4k + 3)/(2k − 1)] + [(6k − 11)/(2k − 1)]
  • [(4k + 3 + 6k − 11)/(2k − 1)]
[(10k − 8)/(2k − 1)]
[(8s + 9)/(3s + 2)] − [(5s − 2)/(3s + 2)]
  • [(8s + 9 − ( 5s − 2 ))/(3s + 2)]
[(3s + 11)/(3s + 2)]
[(7d + 5)/3d] + [(11d − 5)/3d]
  • [(7d + 5 + 11d − 5)/3d]
  • [18d/3d]
6
[6y/(y + 2)] + [12/(y + 2)]
  • [(6y + 12)/(y + 2)]
  • [(6( y + 2 ))/(y + 2)]
6
[6x/(3x + 2)] + [4/(3x + 2)]
  • [(6x + 4)/(3x + 2)]
  • [(2( 3x + 2 ))/(3x + 2)]
2
[21z/(7z − 6)] − [18/(7z − 6)]
  • [(21z − 18)/(7z − 6)]
  • [(3( 7z − 6 ))/(7z − 6)]
3
[(w2 + 11)/(5w − 4)] − [(w2 − 12)/(4 − 5w)]
  • [(w2 + 11)/(5w − 4)] − [(w2 − 12( − 1 ))/(4 − 5w( − 1 ))]
  • [(w2 + 11)/(5w − 4)] − [(( − w2 + 12 ))/(5w − 4)]
  • [(w2 + 11w + w2 − 12)/(5w − 4)]
  • [(5w2 + 11w − 12)/(5w − 4)]
  • [(( 5w − 4 )( w + 3 ))/(5w − 4)]
w + 3

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Adding and Subtracting Rational Expressions with Like Denominators

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Adding with Like Denominators 0:09
    • Example: Regular Numbers
    • Example: Rational Expressions
  • Subtracting with Like Denominators 2:35
    • Example: Regular Fractions
    • Example: Rational Expressions
  • Denominators That Are Additive Inverses 4:08
    • What Are Additive Inverses
    • Example
  • Example 1: Add Rational Expressions 7:54
  • Example 2: Subtract Rational Expressions 8:43
  • Example 3: Add Rational Expressions 10:39
  • Example 4: Subtract Rational Expressions 11:48