Add & Subtract Rationals – Unlike Denominators It is assumed that you understand the material in the three previous modules: 1) Addition and subtraction of rational expressions with common denominators 2) Finding the LCM of two expressions 3) Writing equivalent rational expressions

To add or subtract rational expressions with unlike denominators: 1) Determine the LCD (LCM of the denominators) 2) Write each rational expression as an equivalent rational expression with the LCD as its denominator 3) Add or subtract as you did with common denominators

Example 1 Determine the LCD Add the two rational expressions Note that the denominators are not common

Write each rational as an equivalent expression with the LCD

Write each rational as an equivalent expression with the LCD for the denominator

Add the equivalent rational expressions that now have a common denominator

Since we can’t factor the numerator and nothing can reduced, this is the answer.

Example 2 In the last problem, we went to great detail to find the equivalent rational expressions. Here is a shorter version of the same problem. Add the two rational expressions Determine the LCD

Write the equivalent rational expressions

Since we can’t factor the numerator and nothing can be reduced, this is the answer.

Example 3 Subtract the two rational expressions Note that the denominators are not common Determine the LCD

Write the equivalent rational expressions

Since we can’t factor the numerator and nothing can be reduced, this is the answer.

Example 4 Subtract the two rational expressions Note that the denominators are not common Determine the LCD

Be careful of the sign here