Addition and Subtraction for Rational Functions

Adding and Subtracting Rational Expressions

Today's objectives

• add and subtract rational expressions with like denominators

• factor polynomials

• add and subtract rational expressions with unlike denominators

• find the least common denominator

• simplify rational expressions

Adding and Subtracting with Like Denominators

Ex:  $\frac{7}{4x}+\frac{3}{4x}=\frac{10}{4x}$  

 $=\frac{5}{2x}$  

Multiple Choice

Find the sum:

$$\frac{1}{x}+\frac{9}{x}=$$  

• $$\frac{10}{x}$$  

• $$\frac{10}{2x}$$  

• $$\frac{5}{x}$$  

• $$\frac{10}{x^2}$$  

Multiple Choice

Find the difference:

$$\frac{2x}{x^3-2}-\frac{1}{x^3-2}$$  

• $$\frac{2x-1}{x^3-2}$$  

• $$\frac{2x+1}{x^3-2}$$  

• $$\frac{2x-1}{2x^3-4}$$  

• $$\frac{2x+1}{2x^3-4}$$  

Adding and Subtracting with unlike denominators

• So far, we achieved our first objective, which is to add and subtract rational expressions with like denominators

• Next, we will learn about adding and subtracting rational expressions with unlike denominators

• Follow the steps in order with your teacher

• What questions do you have?

Multiple Choice

Find the sum:

$$\frac{4}{6}+\frac{1}{8}=$$  

• $$\frac{19}{24}$$  

• $$\frac{19}{48}$$  

• $$\frac{5}{14}$$  

• $$\frac{1}{2}$$  

Multiple Choice

Solve

• 5/10

• 7/10

• 1/8

• 10/8

Example of adding rational expressions with unlike denominators

Multiple Choice

Find the sum:

$$\frac{6k}{k+2}+\frac{3}{k+5}=$$  

Multiple Choice

Hint: Factor first

The end!! :D

• Today, you learned to:

• add and subtract rational expressions with like denominators

• add and subtract rational expressions with unlike denominators