### About LCD of 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
LCD of Rational Expressions Practice Test:

#1:

Instructions: Find the Least Common Denominator (LCD).

a) $$\frac{4n + 1}{5n^2 - 20n}\hspace{.2em},\hspace{.2em}\frac{3n}{n^2-16}$$

#2:

Instructions: Find the Least Common Denominator (LCD).

a) $$\frac{5x}{4x+8}\hspace{.2em},\hspace{.2em}\frac{-2}{x^2+3x+2}$$

#3:

Instructions: Find the Least Common Denominator (LCD).

a) $$\frac{8x-7}{12x+60}\hspace{.2em},\hspace{.2em}\frac{17x^4-5}{x^2+5x}\hspace{.2em},\hspace{.2em}\frac{13x^3-4x+19}{x^2+10x+25}$$ $$\frac{8x-7}{12x+60}\hspace{.2em},\hspace{.2em}\frac{17x^4-5}{x^2+5x}\hspace{.2em},$$$$\frac{13x^3-4x+19}{x^2+10x+25}$$

#4:

Instructions: Find the Least Common Denominator (LCD).

a) $$\frac{x-7}{6x^2+7x-3}\hspace{.2em},\hspace{.2em}\frac{12x^4 + 1}{12x^3+14x^2-6x}$$

#5:

Instructions: Find the Least Common Denominator (LCD).

a) $$\frac{5x^4 - 4}{12x^2-31x+7}\hspace{.2em},\hspace{.2em}\frac{-3x^5 + 7x^2 - 11}{40x^2-50x-15}\hspace{.2em},\hspace{.2em}\frac{7x^7}{16x^2-20x-6}$$ $$\frac{5x^4 - 4}{12x^2-31x+7}\hspace{.2em},\hspace{.2em}$$$$\frac{-3x^5 + 7x^2 - 11}{40x^2-50x-15}\hspace{.2em},\hspace{.2em}$$$$\frac{7x^7}{16x^2-20x-6}$$

Written Solutions:

#1:

Solutions:

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

#2:

Solutions:

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

#3:

Solutions:

a) 12x(x + 5)2

#4:

Solutions:

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

#5:

Solutions:

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