Download 01 Simplifying Rational Expressions.notebook

01 Simplifying Rational Expressions.notebook
March 05, 2015
Homework
Worksheet 15-1
Pick a career to research for your paper!!
Vocabulary
Rational Number
A fancy way of saying "fraction"
Expression
An algebraic expression that has a
variable and NO equal sign
Rational Expression
An algebraic fraction
1
01 Simplifying Rational Expressions.notebook
March 05, 2015
Simplify
1.
2.
3. What about: ?
How does relate to factoring?
So, by factoring the numerator, we
were able to cancel a factor from the
numerator with the denominator.
2
01 Simplifying Rational Expressions.notebook
March 05, 2015
Steps for Simplifying Rational Expressions:
1. Factor the Numerator
Factor the Denominator
2. Find all excluded values
for the denominator.
(ie: Values that make the denom zero)
3. Cancel like factors
(ie: Factors in num w/factors in denom)
4. Re­write expression
Notes:
1. Factor the ENTIRE polynomial - NOT numbers.
2. "Excluded Values" are the numbers that make the values in the ( ) in the denominator zero.
3. Only things that are being MULTIPLIED may be
canceled.
4. NEVER, EVER CANCEL PARTS OF SUMS!!!
(This is the ultimate sin in mathematics!!)
3
01 Simplifying Rational Expressions.notebook
March 05, 2015
A sum is any two terms connected
with a "+" sign or a "-" sign in
between them.
x + 5
x
Part of the sum is: The other "part" is:
5
How do you know?
x & 5 are the 2 terms attached by a "+"
The Golden Rule of Algebra:
You can NEVER EVER cancel parts of sums!!
In The Example: x + 5
To NEVER EVER cancel parts of sums means:
You cannot cancel the "x" part or the "5" part, unless you cancel the entire "x + 5" part!!
4
01 Simplifying Rational Expressions.notebook
March 05, 2015
Examples:
because the "5" in the numerator is part of
the sum "x+5" and cannot be canceled with
the 25 in the denominator.
because the 15 & y in the numerator is
NOT a sum, they are parts of a product
(multiplication) which CAN be canceled
with the 3 & y in the denominator.
Sums or Products?
1. x + 3
"+" --> Sum
3. 2x
No "+" --> Product
2. 2x + 6
"+" --> Sum
4. 6 – x
"-" --> Sum
5
01 Simplifying Rational Expressions.notebook
March 05, 2015
Steps for Simplifying Rational Expressions:
1. Factor the Numerator
Factor the Denominator
2. Find all excluded values for the denominator
(ie: Values that make the ( ) in the denom zero)
3. Cancel like factors
(ie: Factors in num w/factors in denom)
4. Re­write expression
Simplify completely (if possible)
and state excluded values
1.
2.
6
01 Simplifying Rational Expressions.notebook
March 05, 2015
Simplify completely (if possible)
and state excluded values
3.
4.
Simplify completely (if possible)
and state excluded values
5.
6.
7
01 Simplifying Rational Expressions.notebook
March 05, 2015
Simplify completely (if possible)
and state excluded values
7.
8.
Simplify completely (if possible)
and state excluded values
9.
10.
8