rational expressions simplifying algebra b. simplifying rational expressions the objective is to be...
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Rational Expressions
Simplifying
Algebra B
Simplifying Rational Expressions
The objective is to be able to simplify a rational expression
5
2x
3
92
x
x
Polynomial – The sum or difference of monomials.
Rational expression – A fraction whose numerator and denominator are polynomials.
Reduced form – a rational expression in which the numerator and denominator have no factors in common.
Our aim is to cancel common factors
Factor the numerator and denominator and then cancel the common factors
We can cancel only factors NOT TERMS
Dividing Out Common Factors
Step 1 – Identify any factors which are common to both the numerator and the denominator.
5
5 7
x
x( )The numerator and denominator have a common factor.
The common factor is the five.
Dividing Out Common FactorsStep 2 – Divide out the common factors.
The fives can be divided since 5/5 = 1
The x remains in the numerator.
The (x-7) remains in the denominator
5
5 7
x
x( ) x
x 7
x
x 7
Factoring the Numerator and Denominator
Factor the numerator.
Factor the denominator.
Divide out the common factors.
Write in simplified form.
3 9
1 2
2
3
x x
x
Factoring
Step 1: Factor the numerator and denominator
3 9
1 2
2
3
x x
x
312
)3(3
x
xx
Divide and Simplify
Step 2: Divide out the common factors. In this case, the common factors divide to become 1.3 3
3 4 2
x x
x x
( )
Step 5: Write in simplified form.
x
x
3
4 2
You Try It
Simplify the following rational expressions.
19
2 4
2
2.
x yz
xyz
23
4 32.
a
a a
33 1 5
7 1 02.
x
x x
42 1 5
1 2
2
2. x x
x x
51 4 3 5 2 1
1 2 3 0 1 8
2
2.
x x
x x
HW Pg. 463 #2 to 30 even