1. MTH 092 Section 12.1 Simplifying Rational Expressions Section 12.2
Multiplying and Dividing Rational Expressions

2. Fractions Again?!?!?!? A rational expression is of the form
Where P and Q are polynomials with Q not equal to 0.

3. Why Can’t Q be equal to 0?
Recall, from our work with slope, that division by 0 is undefined.
If Q is a polynomial, then it has variables.
Those variables cannot take on values that cause Q to become 0.
To figure out what those values are, set Q = 0 and solve.
Key words: undefined, domain

4. Examples
Find any numbers for which each rational expression is undefined:

5. Reducing To Lowest Terms
Recall that reducing a fraction means dividing the numerator and denominator by the same value (usually the greatest common factor).
Reducing a rational expression involves two steps:
Factor both the numerator and denominator.
Cancel common factors.
Cancel factors, not terms.

6. Examples: Reduce to Lowest Terms

7. Multiplying and Dividing
Factor the numerators and denominators completely.
Cancel common factors.
Remember that when you are dividing, you must multiply by the reciprocal of the second rational expression.
You can not cancel terms. You can not cancel parts of terms.

8. Multiply or Divide

9. Opposite Factors Make -1
For all real numbers a and b,
The -1 is usually put in the numerator and can be distributed.

10. Apply “the rule of -1”
Reduce, multiply, or divide as indicated: