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Rational Expressions (LCD) Test
About Finding the LCD for Rational Expressions:

Once we master multiplication and division of rational expressions, we move into addition and subtraction. In order to add or subtract rational expressions, we must first have a common denominator. Our first step to obtaining a common denominator is to identify the LCD for the group.

Test Objectives:

•Demonstrate a general understanding of how to find the LCD

•Demonstrate the ability to factor a polynomial

•Demonstrate the ability to find the LCD for a group of rational expressions

Finding the LCD for a group of Rational Expressions Test:




#1:


Instructions: Find the Least Common Denominator (LCD).


a)


4n + 1 3n
5n2 - 20n  ,  n2 - 16

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#2:


Instructions: Find the Least Common Denominator (LCD).


a)


5x -2
4x + 8  ,  x2 + 3x + 2

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#3:


Instructions: Find the Least Common Denominator (LCD).


a)


8x - 7 17x4 - 5 13x3 - 4x + 19
12x + 60  ,  x2 + 5x  ,  x2 + 10x + 25

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#4:


Instructions: Find the Least Common Denominator (LCD).


a)


x - 7 12x4 + 1
6x2 + 7x - 3  ,  12x3 + 14x2 - 6x

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#5:


Instructions: Find the Least Common Denominator (LCD).


a)


5x4 - 4 -3x5 + 7x2 - 11 7x7
12x2 - 31x + 7  ,  40x2 - 50x - 15  ,  16x2 - 20x - 6

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Written Solutions:




#1:


Solution:


a) 5n(n - 4)(n + 4)


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#2:


Solution:


a) 4(x + 2)(x + 1)


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#3:


Solution:


a) 12x(x + 5)2


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#4:


Solution:


a) 2x(2x + 3)(3x - 1)


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#5:


Solution:


a) 10(2x - 3)(4x + 1)(3x - 7)(4x - 1)


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