Start learning today, and be successful in your academic & professional career. Start Today!

Loading video...

### Dividing Rational Expressions

- When dividing one rational expression by another one, first invert the second rational expression and change the operation from division to multiplication. Then factor all the numerators and denominators, and 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.

### Dividing Rational Expressions

Divide:

[(12x

[(12x

^{2}y^{3}z^{4})/(18xy^{4}z)] ÷[(14x^{4}yz^{2})/(81x^{3}y^{3}z^{3})]- [(12x
^{2}y^{3}z^{4})/(18xy^{4}z)] ×[(81x^{3}y^{3}z^{3})/(14x^{4}yz^{2})] - [(6y
^{2}z^{2})/2y] ×[(9x^{2}z^{2})/(7x^{2})] - [(3yz
^{2})/1] ×[(9z^{2})/7]

[(27yz

^{4})/7]Divide:

[(36a

[(36a

^{2}b^{4}c)/(27a^{4}b^{3}c^{2})] ÷[(48a^{4}b^{2}c^{3})/(54a^{3}b^{5}c^{2})]- [(36a
^{2}b^{4}c)/(27a^{4}b^{3}c^{2})] ×[(54a^{3}b^{5}c^{2})/(48a^{4}b^{2}c^{3})] - [(3b
^{2})/1a] ×[(2b^{2})/(4a^{2}c^{2})]

[(6b

^{4})/(4a^{3}c^{2})]Divide:

[(24j

[(24j

^{3}k^{5}i^{6})/(8j^{5}k^{6}i^{4})] ÷[(60j^{5}k^{2}i^{3})/(40j^{5}k^{2}i)]- [(24j
^{3}k^{5}i^{6})/(8j^{5}k^{6}i^{4})] ÷[(40j^{5}k^{2}i)/(60j^{5}k^{2}i^{3})] - [(2i
^{3})/(1k^{4}i^{3})] ×[1/jk]

[2/(jk

^{5})]Divide:

[(4r − 28)/(10r − 40)] ÷[(7r − 49)/(3r + 15)]

[(4r − 28)/(10r − 40)] ÷[(7r − 49)/(3r + 15)]

- [(4r − 28)/(10r − 40)] ×[(3r + 15)/(7r − 49)]
- [(4( r − 7 ))/(10( r − 4 ))] ×[(3( r + 5 ))/(7( r − 7 ))]
- [4/(10( r − 4 ))] ×[(3( r + 5 ))/7]

[(12( r + 5 ))/(70( r − 4 ))]

Divide:

[(16t + 40)/(21t − 35)] ÷[(10t − 8)/(6t − 10)]

[(16t + 40)/(21t − 35)] ÷[(10t − 8)/(6t − 10)]

- [(16t + 40)/(21t − 35)] ×[(6t − 10)/(10t − 8)]
- [(8( 2t + 5 ))/(7( 3t − 5 ))] ×[(2( 3t − 5 ))/(2( 5t − 4 ))]
- [(8( 2t + 5 ))/7] ×[1/(5t − 4)]

[(8( 2t + 5 ))/(7( 5t − 4 ))]

Divide:

[(26x − 39)/(14x + 30)] ÷[(24x − 36)/(5x − 90)]

[(26x − 39)/(14x + 30)] ÷[(24x − 36)/(5x − 90)]

- [(26x − 39)/(14x + 30)] ×[(5x − 90)/(24x − 36)]
- [(13( 2x − 3 ))/(2( 7x + 15 ))] ×[(5( x − 18 ))/(12( 2x − 3 ))]
- [13/(2( 7x + 15 ))] ×[(5( x − 18 ))/12]

[(65( x − 18 ))/(24( 7x + 15 ))]

Divide:

[(6y − 20)/(16y + 18)] ÷[(36y − 120)/(8y − 36)]

[(6y − 20)/(16y + 18)] ÷[(36y − 120)/(8y − 36)]

- [(6y − 20)/(16y + 18)] ×[(8y − 36)/(36y − 120)]
- [(2( 3y − 10 ))/(2( 8y + 9 ))] ×[(4( 2y − 9 ))/(12( 3y − 10 ))]
- [1/(( 8y + 9 ))] ×[(2( 2y − 9 ))/6]
- [(2( 2y − 9 ))/(6( 8y + 9 ))]

[(2y − 9)/(3( 8y + 9 ))]

Divide:

[(2h − 10)/(4h + 8)] ÷[(2h

[(2h − 10)/(4h + 8)] ÷[(2h

^{2}− 8h − 10)/(2h^{2}+ 7h + 6)]- [(2( h − 5 ))/(4( h + 2 ))] ×[(2h
^{2}+ 7h + 6)/(2( h^{2}− 4h − 5 ))] - [(2( h − 5 ))/(4( h + 2 ))] ×[(( 2h + 3 )( h + 2 ))/(2( h − 5 )( h + 1 ))]
- [1/4] ×[(2h + 3)/(h + 1)]

[(2h + 3)/(4( h + 1 ))]

Divide:

[(2x − x − 15)/(3x + 21)] ÷[(5x − 15)/(2x

[(2x − x − 15)/(3x + 21)] ÷[(5x − 15)/(2x

^{2}+ 8x − 42)]- [(2x − x − 15)/(3x + 21)] ×[(2x
^{2}+ 8x − 42)/(5x − 15)] - [(( 2x + 5 )( x − 3 ))/(3( x + 7 ))] ×[(2( x
^{2}+ 4x − 21 ))/(5( x − 3 ))] - [(( 2x + 5 )( x − 3 ))/(3( x + 7 ))] ×[(2( x + 7 )( x − 3 ))/(5( x − 3 ))]
- [(2x + 5)/3] ×[2/5]

[(2( 2x + 5 ))/15]

Divide:

[(14y + 42)/(14y + 35)] ÷[(2y

[(14y + 42)/(14y + 35)] ÷[(2y

^{2}+ 4y − 6)/(2y^{2}+ 13y + 20)]- [(14y + 42)/(14y + 35)] ÷[(2y
^{2}+ 13y + 20)/(2y^{2}+ 4y − 6)] - [(14( y + 3 ))/(7( 2y + 5 ))] ×[(( 2y + 5 )( y + 4 ))/(2( y
^{2}+ 2y − 3 ))] - [(14( y + 3 ))/(7( 2y + 5 ))] ×[(( 2y + 5 )( y + 4 ))/(2( y + 3 )( y − 1 ))]
- [7/7] ×[(y + 4)/(y − 1)]

[(y + 4)/(y − 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

### Dividing 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 0:10
- Reciprocal of Expression
- Example: Regular Fractions
- Example: Rational Expressions
- Cancel Before Multiplying 3:23
- Why Cancel
- Example
- Rational Expressions Containing Polynomials 6:46
- Example
- Example 1: Divide Rational Expressions 9:15
- Example 2: Divide Rational Expressions 13:11
- Example 3: Divide Rational Expressions 15:39

1 answer

Last reply by: Dr Carleen Eaton

Mon Feb 7, 2011 5:38 PM

Post by Timothy miranda on April 28, 2010

in the cancel before multiplying example all the Z didn't cancel and should be included in the final answer.

3 answers

Last reply by: Dr Carleen Eaton

Wed Nov 2, 2011 9:34 PM

Post by michael egler on February 11, 2010

in example 1. you missed the x^2 the answer should be 5 z^4 x^2 over 4w