About Rational Expressions LCD:
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
#1:
Instructions: Find the LCD.
$$a)\hspace{.2em}\frac{19x}{2x - 6}, \frac{5}{x^2 - 3x}$$
Watch the Step by Step Video Solution View the Written Solution
#2:
Instructions: Find the LCD.
$$a)\hspace{.2em}\frac{5x^2 - 1}{x^2 + 2x - 3}, \frac{2x + 3}{x^2 + 3x}$$
Watch the Step by Step Video Solution View the Written Solution
#3:
Scroll Right for More »
Instructions: Find the LCD.
$$a)\hspace{.2em}\frac{3x^2 - 5x + 7}{x^2 - x - 2}, \frac{x^3 + 5x^2 - 4x - 20}{x^2 + 7x + 10}$$
Watch the Step by Step Video Solution View the Written Solution
#4:
Instructions: Find the LCD.
Scroll Right for More »
$$a)\hspace{.2em}\frac{4x}{3x^2}, \frac{2x - 1}{6x^2 - 42x}, \frac{3x^2 - 10x + 9}{2x^3 + x^2}$$
Watch the Step by Step Video Solution View the Written Solution
#5:
Instructions: Find the LCD.
Scroll Right for More »
$$a)\hspace{.2em}\frac{4x^2 - 1}{x^2 - 9}, \frac{2x - 9}{x^2 + 2x - 3}, \frac{5x^2 - 7x + 1}{x^3 - 4x^2 + 3x}$$
Watch the Step by Step Video Solution View the Written Solution
Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}2x(x - 3)$$
Watch the Step by Step Video Solution
#2:
Solutions:
$$a)\hspace{.2em}x(x - 1)(x + 3)$$
Watch the Step by Step Video Solution
#3:
Solutions:
$$a)\hspace{.2em}(x - 2)(x + 1)$$
Watch the Step by Step Video Solution
#4:
Solutions:
$$a)\hspace{.2em}6x^2(x - 7)(2x + 1)$$
Watch the Step by Step Video Solution
#5:
Solutions:
$$a)\hspace{.2em}x(x + 3)(x - 3)(x - 1)$$
