Finding the LCD and Solving an Algebraic Equation or Inequality

1. Re-write each denominator as a product of prime factors. This may require the use of : a. a) simply factoring out the GCF b. b) recognizing the polynomial as a special product such as the difference of two squares c. c) utilizing the AC method to factor a trinomial, or 1. d) factoring by grouping Each of these methods is discussed on the “Factoring Polynomials” handout. 2. Make a list of each unique denominator found in any of the denominators that you factored out in step 1

Count the number of times each unique factor is used in any ONE denominator.

The greatest number of times that factor appears in any ONE denominator is the number of times it must appear in the LCD.

2. REMEMBER: In algebra, we are never subtracting, so change the subtraction sign to an addition sign and place the negative sign in the algebraic expression that follows. Most often this sign will be attached to the numerator, but when it is necessary, it can be placed in the denominator. WATCH OUT for numerators and denominators that are polynomials LCD = when you move the minus sign to either of these. USE PARENTHESES!!! 3. Place parentheses at both ends of the algebraic equation or inequality.

Place the LCD to the left side of the algebraic equation or inequality.

Distribute the LCD through the algebraic equation or inequality, cross reducing like factors between the LCD numerator and the corresponding denominator of each fraction within the algebraic equation or inequality. This should result in “reducing” all of the numerators of the original algebraic equation or inequality to “whole numbers”.

4. Follow the properties of equality and solve for the variable.

3. Check your solution.