1. Rational Expressions
6.1

2. Factors are things that are multiplied.
The expression
is one term (monomial).
It has four factors.
Factors are things that are multiplied.
How many factors?
six

3. How many terms?
How many terms?
TWO
TWO
How many factors?
How many factors?
TWO
TWO
or, FOUR
Monomials can be factored into “pieces”.

4. SIMPLIFYING RATIONAL EXPRESSIONS

5. In elementary school, we learned to cancel fractions for “one
In elementary school, we learned to cancel fractions for “one.” This technique is also used in “reducing” fractions. 2 1 4 3 1 3 2 7 1 1

6. Sing! We have rational expressions That must be simplified.
Tune: I’ve been workin’ on the railroad.
We have rational expressions
That must be simplified.
One main rule we have to follow:
Cancel what is multiplied.
We need factors.
We must factor.
GCF is first!
Difference of two squares, grouping,
Also FOIL reversed.

7. NO!! GCF is first! We need factors. We must factor.
We have rational expressions that must be simplified. One main rule we have to follow: cancel what is multiplied.
NO!!
We need factors.
We must factor.
GCF is first!

8. FOIL Reversed GCF is first Difference of two squares Doesn’t need
factoring
FOIL
Reversed

9. FOIL Reversed GCF is first Difference of two squares Doesn’t need
factoring
FOIL
Reversed

10. There is only one monomial, so it cannot be cancelled:
We are dividing out fractions for “one.”

11. Steps for simplifying:
Put each polynomial in descending order
Look for a GCF. If the first term is negative, factor out a negative.
Then factor using FOIL, Grouping, DOTS, etc.

12. Steps for simplifying:
Then cancel. You can cancel pieces of monomials with similar pieces of other monomials, but binomials can only be cancelled if they are exactly alike.

13. Example: Put each polynomial in descending order
Factor out the GCF first:
Continue factoring:

14. First cancel pieces of monomials:
Then cancel exact binomials:
Write answer as one fraction: