1. Rational Expressions and Equations
Module 7
Rational Expressions and Equations

2. Simplifying Rational Expressions
Video Links
Simplifying Rational Expressions
Adding and Subtracting Rational Expressions
Multiplying and Dividing Rational Expressions
Solving Rational Expressions

3. Simplifying Rational Expressions
Find the common factors from the numerator and denominator, then cancel like factors.
You may have to factor a binomial or trinomial in order for something to cancel out.

4. Another example & Video Link

5. Multiplying Rational Expressions
Factor the numerator and denominator of both rational expressions.
Find what will cancel in the cross products or in each rational expression.

6. Dividing Rational Expressions
Keep Change Flip
Keep the first fraction
Change to multiplication
Flip the second fraction
Factor the numerator and denominator of both rational expressions. Find what will cancel in the cross products or in each rational expression.

7. Adding and Subtracting Expressions

8. Another Example (unlike Denominators) & Video Link

9. Complex Fractions
Complex fractions can be rewritten as a division problem (with the top fraction first and the bottom fraction second. Follow the rules for dividing rational expressions and solve.

10. Solving Rational Expressions
When two rational expressions are equal, use cross products to get rid of the denominators. Then solve like a regular equation.

11. Another Example
The first step is to get the LCD (least common denominator). Once everything has a common denominator, follow the operations so that the denominators will cancel out. Finally, rewrite the equation so it is set to zero and find the solution(s).