Rational Expressions 6.1

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

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

SIMPLIFYING RATIONAL EXPRESSIONS

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

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.

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!

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

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

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

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.

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.

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

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