Title: Lesson 1–1
Author: Teri Willard
Last saved by: Glencoe Mathematics

Lesson 8–2

Example 1  LCM of Monomials
Find the LCM of 10ab^2, 105a^3b^2c, and 50ab^2c^3.

10ab^2 = 2 • 5 • a • b^2	Factor the first monomial.
105a^3b^2c = 3 • 5 • 7 • a^3 • b^2 • c	Factor the second monomial.
50ab^2c^3 = 2 • 5^2 • a • b^2 • c^3	Factor the third monomial.
LCM = 2 • 3 • 5^2 • 7 • a^3 • b^2 • c^3	Use each factor the greatest number of times
	= 1050a^3b^2c^3	it appears as a factor and simplify.

Example 2  LCM of Polynomials
Find the LCM of 2x^3 – 9x^2 – 5x and x^4 – 10x^3 + 25x^2.

2x^3 – 9x^2 – 5x = x(2x + 1)(x – 5)	Factor the first polynomial.
x^4 – 10x^3 + 25x^2 = x^2(x – 5)^2	Factor the second polynomial.
LCM = x^2(2x + 1)(x – 5)^2	Use each factor the greatest number of times
	it appears as a factor.

Example 3  Monomial Denominators
Simplify  – .

 –  =  – 	The LCD is 50a^2b^2c^2. Find equivalent
	fractions that have this denominator.
	=  – 	Simplify each numerator and denominator.
	= 	Subtract the numerators.

Example 4  Polynomial Denominators
Simplify  + .

 +  
=  + 	Factor the denominators.
=  + 	The LCD is 2(a – 2)(a + 1)(a + 3).
=  + 	Distributive Property
= 	Add the numerators.
= 	Combine like terms.
=  or 	Simplify.

Example 5  Simplify Complex Fractions
Simplify .
 = 	The LCD of the numerator is (a – 2)(a + 1).
	= 	Simplify the numerator.
	=  ÷ 	Write as a division expression.
	=  • 	Multiply by the reciprocal of the divisor.
	=  • 	Simplify.
	= a – 1

Example 6  Use a Complex Fraction to Solve a Problem
GEOMETRY An expression for the area of a parallelogram in terms of a and b is . An expression for the length of the base is . Find the height of the parallelogram.

A = bh	Formula for the area of a parallelogram
h = 	Solve the formula for h.
= 	A = , b = 
=  ÷ 	Write as a division expression.
=  • 	Multiply by the reciprocal of the divisor.
=  • 	Factor.
= 	Simplify.

The height of the parallelogram is .