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 | |
5n^{2} - 20n | , | n^{2} - 16 |
#2:
Instructions: Find the Least Common Denominator (LCD).
a)
5x | -2 | |
4x + 8 | , | x^{2} + 3x + 2 |
#3:
Instructions: Find the Least Common Denominator (LCD).
a)
8x - 7 | 17x^{4} - 5 | 13x^{3} - 4x + 19 | ||
12x + 60 | , | x^{2} + 5x | , | x^{2} + 10x + 25 |
#4:
Instructions: Find the Least Common Denominator (LCD).
a)
x - 7 | 12x^{4} + 1 | |
6x^{2} + 7x - 3 | , | 12x^{3} + 14x^{2} - 6x |
#5:
Instructions: Find the Least Common Denominator (LCD).
a)
5x^{4} - 4 | -3x^{5} + 7x^{2} - 11 | 7x^{7} | ||
12x^{2} - 31x + 7 | , | 40x^{2} - 50x - 15 | , | 16x^{2} - 20x - 6 |
Written Solutions:
Solution:
a) 5n(n - 4)(n + 4)
Solution:
a) 4(x + 2)(x + 1)
Solution:
a) 12x(x + 5)^{2}
Solution:
a) 2x(2x + 3)(3x - 1)
Solution:
a) 10(2x - 3)(4x + 1)(3x - 7)(4x - 1)