Summary Algebra Math : Multiply and Divide Rational Expressions

MULTIPLYING RATIONAL EXPRESSIONS
To Multiply Two Fractions
  ·
·
, 0 and 0
  ·

 
Example 1 Multiply:

 
Solution: First divide out any common factors to both a numerator and a
denominator; then multiply.
1
3 2 1 · 2 2
·


5 9 5·3 15
3
The same principles apply when multiplying rational expressions containing variables.
Before multiplying, you should first divide out any common factors to both a numerator and a
denominator.

To Multiply Rational Expressions
1. Factor all numerators and denominators completely.
2. Divide out common factors.
3. Multiply numerators together and multiply denominators together.

Example 2 Multiply: ·
 
1  2 (
Solution: 3  4(  3  4( 
·
·
2( 
2( 3 2( 3
1 1 1 1

Example 3 Multiply:   5 ·  
Solution: 7 5 7 7
  5 · 
·

  5  1     5  
 
Example 4 Multiply: ·
  
Solution:  * 2 1 1
3  * 2 * 2 3 *2
· 
·

6   4 6   * 2  2 2  2
2 

Note: When multiplying rational expressions, if only the signs differ in a numerator and a
denominator (for instance, the numerator is x-7 & the denominator is 7-x), factor out 1 from either
the numerator or denominator; then divide out the common factor.
 (  ( (
·
·

   1   
 
Example 5 Multiply: ·
 
Solution: 3 * 2 4  8 3 * 2 41  2 3 * 2 412  1 4
·
·
·

4
2  1 3 * 2 2  1 3 * 2 2  1 3 * 2 1
   
Example 6 Multiply: ·
  
  2  3 * 5 2  1 * 1 2  3 * 5 2  1 * 1
2 * 7  15 2 *   1
·
·
·
1
4   8 * 3   * 6 * 5 2  32  1  * 5 * 1 2  32  1  * 5 * 1