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
Rational Expressions LCD Practice Test:

#1:

Instructions: Find the LCD.

$$a)\hspace{.2em}\frac{19x}{2x - 6}, \frac{5}{x^2 - 3x}$$

#2:

Instructions: Find the LCD.

$$a)\hspace{.2em}\frac{5x^2 - 1}{x^2 + 2x - 3}, \frac{2x + 3}{x^2 + 3x}$$

#3:

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Instructions: Find the LCD.

$$a)\hspace{.2em}\frac{3x^2 - 5x + 7}{x^2 - x - 2}, \frac{x^3 + 5x^2 - 4x - 20}{x^2 + 7x + 10}$$

#4:

Instructions: Find the LCD.

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$$a)\hspace{.2em}\frac{4x}{3x^2}, \frac{2x - 1}{6x^2 - 42x}, \frac{3x^2 - 10x + 9}{2x^3 + x^2}$$

#5:

Instructions: Find the LCD.

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$$a)\hspace{.2em}\frac{4x^2 - 1}{x^2 - 9}, \frac{2x - 9}{x^2 + 2x - 3}, \frac{5x^2 - 7x + 1}{x^3 - 4x^2 + 3x}$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}2x(x - 3)$$

#2:

Solutions:

$$a)\hspace{.2em}x(x - 1)(x + 3)$$

#3:

Solutions:

$$a)\hspace{.2em}(x - 2)(x + 1)$$

#4:

Solutions:

$$a)\hspace{.2em}6x^2(x - 7)(2x + 1)$$

#5:

Solutions:

$$a)\hspace{.2em}x(x + 3)(x - 3)(x - 1)$$