rational expressions packet -...
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Name: Date: Period: Math Stretch: Factor the following expressions completely: a) π₯! β 16 b) π₯! + 2π₯
c) π₯! β 4π₯ β 12 c) 3π₯! + 10π₯ β 8
Notes: Simplifying Rational Expressions A rational expression is in simplest form when: Let a, b and c be nonzero real numbers or variable expressions. Then the following property applies:
To simplify a rational expression: Example 1: Simplify the expression below completely:
Example 2: Simplify the expression below completely:
π¦! β 3π¦! β 18π¦2π¦! + 5π¦ + 3
Simplifying Practice:Simplify the expression, if possible. State the domain of the function (excluded values).
1)!!!!!
2) !!!!"!!!!!!!!!!!
3) !!!!!!!!!!
4) !!!!!!!!!!!!"
5) (!!!)(!!!)(!!!)(!!!)
6) !!!!!!!!"!!!
7) Write a rational expression that has a domain of π₯ β 3 and simplifies to π₯ + 5:
Notes: Multiplying & Dividing Rational Expressions To multiply rational expressions, multiply the __________________________ and then multiply the ___________________________. Simplify if possible.
Example:
To divide rational expressions. Multiply the first expression by the _________________________ of the second expression.
Example:
Multiplying and Dividing Practice:
Multiply or divide the expression and simplify completely:
1) !!!
!!β !!
!!!!!
2) !!!!!!!!!!!!!!
β !!!!!!!"!!!!
3) !!!!!!!!!!
Γ· !!!!!!!!!!!
4) π₯! + 9π₯ + 18Γ· !!!!!!!"!!!!!!!"
Notes: Adding & Subtracting Rational Expressions To add (or subtract) rational expressions with like denominators, simply add (or subtract) their ________________________. Then place the result over the common denominator.
Example with like denominators:
To add (or subtract) two rational expressions with UNLIKE denominators: Find the ______________ ___________________ _______________________ (LCD), which is the
_______________ __________________ ___________________ (LCM) of the denominators.
Example 1 with unlike denominators:
ππ+
ππβ π
Example 2 with unlike denominators:
πππβ πβ
π+ πππ β π
Example 3 with unlike denominators:
What is the sum of π
π!π and
ππ!π
Adding and Subtracting Practice: Add or subtract the expression and simplify completely: 1) !
!!!!+ !
!!!! 2) !
!!!!!!!+ !
!!!
3) !!!!!
β !!!!!"
4) !!!!!!
β !!!!!
5) !!!!"!"!!!
+ !!!!
6) !!!!!!!!!!
+ !!!!!!!!!!"
+ !!!!!!!!