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## Practice Questions

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### Rational Expressions

- A
*rational expression*is a fraction whose numerator and denominator are polynomials. - Any values of the variable that make the denominator equal to zero produce an undefined expression. So these values must be
*excluded*when we consider the rational expression. - To
*simplify*a rational expression, factor the numerator and denominator completely. Then cancel the common factors. - 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.
- Excluded values are always determined using the
*original*expression, not the simplified one.

### Rational Expressions

Find the excluded values:

[(x

[(x

^{2}− 11x + 28)/(x^{2}− 2x + 35)]- x
^{2}− 2x + 35 = 0 - (x − 7)(x + 5) = 0

Excluded values = 7, − 5

Find the excluded values:

[(y

[(y

^{2}+ 10 + 24)/(y^{2}+ 15y + 36)]- y
^{2}+ 15y + 36 = 0 - (y + 12)(y + 3) = 0

Excluded values = − 12, − 3

Find the excluded values:

[(z

[(z

^{2}− 5z − 24)/(z^{2}− 2z − 63)]- (z − 9)(z + 7)

Excluded values = 9, − 7

Simplify and find the excluded values:

[(12x

[(12x

^{2}y^{4})/(36xy^{2})]- [(12xy
^{2}(xy^{2}))/(12xy^{2}(3))] - [(xy
^{2})/3]

Excluded values:

36xy

36xy

^{2}= 0, xy^{2}= 0, x = 0, y = 0Simplify and find the excluded values:

[(18a

[(18a

^{2}b^{3}c^{5})/(48a^{4}bc^{4})]- [(3a
^{2}bc^{4}(6b^{2}c))/(3a^{2}bc^{4}(16a^{2}))] - [(6b
^{2}c)/(16a^{2})] - Excluded values: a
^{4}bc^{4} - a = 0, b = 0, c = 0

[(6b

Exclude values: a = 0, b = 0, c = 0

^{2}c)/(16a^{2})]Exclude values: a = 0, b = 0, c = 0

Simplify and find the excluded values:

[(50d

[(50d

^{3}e^{4}f^{2})/(15d^{2}e^{2}f^{2})]- [(5d
^{2}e^{2}f^{2}(10de^{2}))/(5d^{2}e^{2}f^{2}(3))] - [(10de
^{2})/3]

Excluded values: d = 0, e = 0, f = 0

Simplify and find the excluded values:

[(6y + 24)/(2y

[(6y + 24)/(2y

^{2}+ 2y − 24)]- [(6(y+4))/(2(y
^{2}+y−12))] - [(6(y+4))/(2(y+4)(y−3))]
- [3/(2(y−3))]
- Excluded Values: 2y
^{2}+2y−24 - 2(y+4)(y−3)=0

y=−4, 3

Simplify and find the excluded values:

[(4y + 8)/(3y

[(4y + 8)/(3y

^{2}− 12y − 36)]- [(4(y + 2))/(3(y
^{2}− 4y − 12))] - [(4(y + 2))/(3(y + 2)(y − 6))]
- [4/(3(y − 6))]
- Excluded values: 3y
^{2}− 12y − 36 = 0 - 3(y + 2)(y − 6) = 0

y = − 2,6

Simplify and find the excluded values:

[(2x

[(2x

^{2}− 10x − 48)/(4x^{2}+ 20x + 24)]- [(2(x
^{2}− 5x − 24))/(2(2x^{2}+ 10x + 12))] - [((x−8)(x+3))/((2x+4(x+3))]
- [(x − 8)/(2x + 4)]
- Excluded values:4x
^{2}+ 20x + 24 = 0 - 2(2x
^{2}+10x+12)=0 - 2(2x+4)(x+3)=0
- 2x + 4 = 0
- x = − 2
- x + 2 = 0

x = − 3

Simplify and find the excluded values:

[(4x

[(4x

^{2}− 4x − 8)/(3x^{2}− 2x − 8)]- [(4(x
^{2}−x−2))/(3x^{2}−2x−8)] - [(4(x−2)(x+1))/((3x+4)(x−2))]
- [((4x+1))/((3x+4))]
- Excluded values: 3x
^{2}− 2x − 8 = 0 - (3x + 4)(x − 2) = 0
- 3x + 4 = 0
- x = − [4/3]
- x − 2 = 0

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

### 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
- Rational Expressions 0:10
- Examples
- Excluded Values 1:03
- Dividing by 0
- Example
- Simplifying Rational Expressions 7:12
- Eliminating the GCF
- Example: Regular Fraction
- Example: Rational Expression
- Simplifying and Excluded Values 10:15
- Original Rational Expression
- Example
- Example 1: Find Excluded Values 13:47
- Example 2: Simplify and Find Excluded Values 16:10
- Example 3: Simplify and Find Excluded Values 22:04
- Example 4: Simplify and Find Excluded Values 26:29

0 answers

Post by claire cooper on December 8, 2014

Oops sorry I wrote it down wrong and I don't know how to edit.

The question is correct ex pet the denominator it is suppose to be 12c+72

1 answer

Last reply by: Dr Carleen Eaton

Mon Dec 15, 2014 11:43 PM

Post by claire cooper on December 8, 2014

Hi I'm watching these videos they are great by the way. I am havinging troubles simplifying my home work .

My problem is is this

Simplify the rational expression

4c^+8c,-96/12c+92

Can some help me with this please and thank you?