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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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Complex Fractions

  • A complex fraction is a fraction with one or more fractions in the numerator or the denominator (or both).
  • If a complex fraction consists of one fraction divided by another fraction, simplify the complex fraction by dividing the fraction in the numerator by the fraction in the denominator: invert the fraction in the denominator and multiply it by the fraction in the numerator.
  • If the expression in either the numerator or denominator of the complex fraction consists of a sum or difference of fractions, carry out that sum or difference first and simplify the result. Then simplify the resulting complex fraction using the technique described above.

Complex Fractions

Write as a rational expression:
4e2 − 3 − [(e + 1)/(e + 5)]
  • [(( e + 5 ) ×( 4e2 − 3 ))/(( e + 5 ) ×1)] − [(e + 1)/(e + 5)]
  • [(4e2 − 3e + 20e2 − 15)/(e + 5)] − [(e + 1)/(e + 5)]
  • [(4e2 − 3e + 20e2 − 15 − e − 1)/(e + 5)]
[(4e2 + 20e2 − 4e − 16)/(e + 5)]
Write as a radical expression:
7a2 − 10 + [(a − 8)/(a + 6)]
  • [(( a + 6 ) ×( 7a2 − 10 ))/(( a + 6 ) ×1)] + [(a − 8)/(a + 6)]
  • [(7a3 − 10a + 42a2 − 60 + a − 8)/(a + 6)]
[(7a3 + 42a2 − 9a − 68)/(a + 6)]
Write as a radical expression:
12b2 + 3 − [(b + 5)/(b − 1)]
  • [(( b − 1 )( 12b2 + 3 ))/(( b − 1 )( 1 ))] − [(b + 5)/(b − 1)]
[(12b3 + 3b − 12b2 − 3 − b − 5)/(b − 1)]
Simplify:
[[([(x2)/(y2)])/([(3x + 1)/(4x − 5)])]]
  • [([a/b])/([c/d])] = [ad/bc]
  • [(x2( 4x − 5 ))/(y2( 3x + 1 ))]
[(4x3 − 5x2)/(3xy2 + y2)]
Simplify:
[[([x/(y3)])/([(7x − y)/(6x + 11y)])]]
  • [(x( 6x + 11y ))/(y3( 7x − y ))]
[(6x2 + 11xy)/(7xy3 − y4)]
Simplify:
[([(m2)/n])/([(m + n2)/(2m − n2)])]
  • [(m2( 2m − n2 ))/(n( 2m − n2 ))]
[(2m3 − m2n2)/(2mn − n3)]
Simplify:
[([(x2 + 3x − 4)/(x2 + 5x + 6)])/([(x2 − 5x + 4)/(x2 − 2x − 8)])]
  • [(x2 + 3x − 4)/(x2 + 5x + 6)] ×[(x2 − 2x − 8)/(x2 − 5x + 4)]
[[(x + 4)/(x + 3)]]
Simplify:
[([(x2 + 12x + 35)/(x2 + 8x + 12)])/([(x2 − 25)/(x2 − 3x − 10)])]
  • [(x2 + 12x + 35)/(x2 + 8x + 12)] ×[(x2 − 3x − 10)/(x2 − 25)]
  • [(( x + 7 )( x + 5 ))/(( x + 2 )( x + 6 ))] ×[(( x − 5 )( x + 2 ))/(( x + 5 )( x − 5 ))]
[(x + 7)/(x + 6)]
Simplify:
[([(x2 − 64)/(x2 + 5x − 24)])/([(x2 + x − 72)/(x2 + x − 12)])]
  • [(x2 − 64)/(x2 + 5x − 24)] ×[(x2 + x − 12)/(x2 + x − 72)]
  • [(( x − 8 )( x + 8 ))/(( x + 8 )( x − 3 ))] ×[(( x − 3 )( x + 4 ))/(( x − 8 )( x + 9 ))]
[(x + 4)/(x + 9)]
Simplify:
[([(x + 6)/(x2 + 12x + 20)])/([(x + 1)/(x2 + x − 2)])]
  • [(x + 6)/(x2 + 12x + 20)] ×[(x2 + x − 2)/(x + 1)]
[(( x + 6 )( x2 + x − 2 ))/(( x2 + 12x + 20 )( x + 1 ))]

*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

Complex Fractions

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
  • Mixed Expressions 0:10
    • Analogy to Mixed Fractions
    • Polynomial and Rational Expression
    • Example: Combining
    • Converting to Rational Expression
  • Complex Fraction 5:16
    • Examples
  • Simplifying Complex Fractions 6:08
    • Example
  • Example 1: Write as Rational Expression 9:43
  • Example 2: Simplify Complex Fractions 12:44
  • Example 3: Simplify Complex Fractions 15:03
  • Example 4: Simplify Complex Fractions 19:55