﻿ GreeneMath.com - Finding the Least Common Denominator (LCD) for a Group of Rational Expressions Test
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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