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)
 0 answersPost by Hossain Khondaker on April 12, 2015I am having a difficult time comprehending this chapter I am  struggling with the whole chapter please help me. 1 answerLast reply by: Dr Carleen EatonSat Jul 27, 2013 10:15 AMPost by Edwin Wong on July 12, 2013it should be (x+2) not (x+5)

### Multiplying Rational Expressions

• To multiply two rational expressions, first factor all the numerators and denominators. Then cancel the common factors. Combine the remaining factors to form the final, simplified answer.
• If two factors in the numerator and denominator look almost the same, factor –1 out of either of the factors and see if you get two identical factors.

### Multiplying Rational Expressions

Multiply:
[(40a2b3c5)/(20a3b5c4)] ×[(15a4b3c2)/(24a2b5c3)]
• [(1c2)/(4b2c2)] ×[3a/(6b2)]
• [1/(4b2)] ×[a/(2b2)]
• [a/(4b2 ×2b2)]
[a/(8b4)]
Multiply:
[(18u4v3w5x8)/(26v4w6x2)] ×[(14v5w2x4)/(54u3v6w7)]
• [(1ux8)/(13w4)] ×[(7vx2)/(3v3w2)]
• [(ux8)/(13w4)] ×[(7x2)/(3v2w5)]
[(7ux10)/(39v2w9)]
Multiply:
[(42c3d2e4)/(60c5d6e2)] ×[(45c6e2f3)/(35d4ef2)]
• [(6c3)/(4d6)] ×[(3cf3)/(5d2ef2)]
• [(3c3)/(2d6)] ×[3cf/(5d2e)]
[(9c4f)/(10d8e)]
Multiply:
[(6y + 36)/(4y − 14)] ×[(16y + 30)/(2y + 12)]
• [(6( y + 6 ))/(2( 2y − 7 ))] ×[(2( 8y + 15 ))/(2( y + 6 ))]
• [3/(2y − 7)] ×[(8y + 15)/1]
[(3( 8y + 15 ))/(2y − 7)]
Multiply:
[(24n − 36)/(10n − 35)] ×[(16n + 48)/(18n − 27)]
• [(12( 2n − 3 ))/(5( 2n − 7 ))] ×[(16( n + 3 ))/(9( 2n − 3 ))]
• [12/(5( 2n − 7 ))] ×[(16( n + 3 ))/9]
[4/(5( 2n − 7 ))] ×[(16( n + 3 ))/3]
Multiply:
[(16b + 44)/(27b − 45)] ×[(15b − 25)/(16b − 72)]
• [(4( 4b + 11 ))/(9( 3b − 5 ))] ×[(5( 3b − 5 ))/(8( 2b − 9 ))]
[(( 4b + 11 ))/9] ×[5/(( 2b − 9 ))]
Multiply:
[(9x + 12)/(4x + 20)] ×[(x2 + 3x − 10)/(3x2 + x − 4)]
• [(3( 3x + 4 ))/(4( x + 5 ))] ×[(( x + 5 )( x − 2 ))/(( 3x + 4 )( x − 1 ))]
• [3/4] ×[(x − 2)/(x − 1)]
[(3( x − 2 ))/(4( x − 1 ))]
Multiply:
[(6x − 21)/(6x − 24)] ×[(5x2 + 25x + 20)/(2x2 + x − 28)]
• [(3( 2x − 7 ))/(6( x + 4 ))] ×[(5( x2 + 5x + 4 ))/(2x2 + x − 28)]
• [(3( 2x − 7 ))/(6( x + 4 ))] ×[(5( x + 4 )( x + 1 ))/(( 2x − 7 )( x + 4 ))]
• [3/6] ×[(5( x + 1 ))/(( x + 4 ))]
• [1/2] ×[(5( x + 1 ))/(( x + 4 ))]
[(5( x + 1 ))/(2( x + 4 ))]
Multiply:
[(x2 − 12x + 32)/(4x2 − 16x − 20)] ×[(2x2 − 50)/(2x2 − 15x − 8)]
• [(( x − 4 )( x − 8 ))/(4( x2 − 4x − 5 ))] ×[(2( x2 − 25 ))/(2x2 − 15x − 8)]
• [(( x − 4 )( x − 8 ))/(4( x + 1 )( x − 5 ))] ×[(2( x + 5 )( x − 5 ))/(( 2x + 1 )( x − 8 ))]
• [(x − 4)/(4( x + 1 ))] ×[(2( x + 5 ))/(2x + 1)]
• [(x − 4)/(2( x + 1 ))] ×[(x + 5)/(2x + 1)]
[(( x − 4 )( x + 5 ))/(2( x + 1 )( 2x + 1 ))]
Multiply:
[(2x2 − 10x − 28)/(x2 − 2x − 80)] ×[(5x2 − 36x − 32)/(6x2 − 12)]
• [(2( x2 − 5x − 14 ))/(x2 − 2x − 80)] ×[(5x2 − 36x − 32)/(6( x2 − 2 ))]
[(2( x + 2 )( x − 7 ))/(( x − 10 )( x + 8 ))] ×[(( 5x + 4 )( x − 8 ))/(6( x + 2 )( x − 2 ))]

*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

### Multiplying Rational Expressions

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
• Procedure 0:08
• Examples
• Cancel Before Multiplication 1:53
• Example
• Rational Expressions Containing Polynomials 3:18
• Example
• Example 1: Multiply Rational Expressions 6:04
• Example 2: Multiply Rational Expressions 9:11
• Example 3: Multiply Rational Expressions 11:19
• Example 4: Multiply Rational Expressions 17:36