Factoring trinomials (a≠1), operations on rational expressions, non-permissible values.

1. More about
Rational Expressions
Reduced Speed Ahead
by flickr user taberandrew

2. Operations on Rational Expressions
... follow the same rules as operations on fractions (rational numbers)
(alt
hou
I Addition and Subtraction a quot;re gh
nym ally we
ore quot; su don
• find a common denominator in h btra 't
• add or subtract as required igh ct
sch
(watch your signs!) ool
)

3. SIGNS

4. Operations on Rational Expressions
... follow the same rules as operations on fractions (rational numbers)
II Mulitplication Re
me
the mb
• factor and reduce to simplest form wit num er!
h a era Any f
• multiply numerators, then denominators den ny tor act
om fact can or in
ina or i
tor n th reduc
e e
factor out a -1

5. Factor out -1

6. Operations on Rational Expressions
... follow the same rules as operations on fractions (rational numbers)
III Division
of h ere!)
• multiply the numerator by the reciprocal TS ions
of the denominator (LO trict
res

7. Reducing

9. RESTRICTIONS!
We quot;restrictquot; the variable (i.e. list
the non-permissable values) to
ensure there is no division by zero.
I Addition and Subtraction
• restrict the denominators
Don't upset the
Math Ninja.
She's got a stick.

10. RESTRICTIONS!
We quot;restrictquot; the variable (i.e. list
the non-permissable values) to
ensure there is no division by zero.
II Multiplication
• restrict the denominators
Don't upset the
Math Ninja.
She's got a stick.

11. RESTRICTIONS!
We quot;restrictquot; the variable (i.e. list
the non-permissable values) to
ensure there is no division by zero.
III Division
• restrict everything except the
numerator of the first fraction
Don't upset the
Math Ninja.
She's got a stick.

12. First: Factor
Second: Restrictions?
Third: Reduce
Do you understand?
Compare the graphs ...

13. First: Factor
Second: Restrictions?
Third: Reduce
Do you understand?
Compare the graphs ...