simplifying rational expressions
DESCRIPTION
TRANSCRIPT
Divide out the common factors
Factor the numerator and denominator and then divide the common factors
+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 Factors
Step 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: Look for common factors to both terms in the numerator.
3 9
1 2
2
3
x x
x
3 is a factor of both 3 and 9.
X is a factor of both x2 and x.Step 2: Factor the numerator.
3 9
1 2
2
3
x x
x
3 3
12 3
x x
x
( )
+Factoring
Step 3: Look for common factors to the terms in the denominator and factor.
3 9
1 2
2
3
x x
x
The denominator only has one term. The 12 and x3 can be factored.
The 12 can be factored into 3 x 4.
The x3 can be written as x • x2.3 9
1 2
2
3
x x
x
3 3
3 4 2
x x
x x
( )
+
Divide and Simplify
Step 4: 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