Transcript 3.8 Simplify Rational Expressions Vocabulary Rational

3.8
Simplify Rational Expressions
Vocabulary
Rational
Expression
An expression that can be written as
a ratio of two polynomials.
A number that makes a rational
Excluded Value expression undefined.
A rational expression when the
Simplest form of a
numerator and denominator have
rational expression
no factors in common other than 1.
3.8
Simplify Rational Expressions
Example 1 Find excluded values
Find the excluded values, if any, of the expression.
x
a.
4x  8
a. The expression
3x
b. 2
x  16
x
4x  8
1
c. 2
x 2
is undefined when ________
4 x  8 = 0,
or x = ___,
2 the excluded value is _____.
2
3.8
Simplify Rational Expressions
Example 1 Find excluded values
Find the excluded values, if any, of the expression.
x
a.
4x  8
b. The expression
3x
b. 2
x  16
3x
2
x  16
1
c. 2
x 2
2
is undefined when ________
x  16 = 0,
or (______)(_______)
x  4 x  4 = 0.
The solutions to the of the equation are ____
4
4 and ____.
The excluded values are ____
4
4 and ____.
3.8
Simplify Rational Expressions
Example 1 Find excluded values
Find the excluded values, if any, of the expression.
x
a.
4x  8
c. The expression
3x
b. 2
x  16
1
2
x 2
1
c. 2
x 2
2
is undefined when ________
x  2 = 0.
The graph of y = x2 + 2 ________________________.
does not cross the x-axis
So, the quadratic equation has _____________.
no real roots
no excluded values
There are ___________________.
Simplify Rational Expressions
3.8
Checkpoint. Find the excluded values, if any, of the
expression.
x6
1.
14 x
14 x  0
14 14
x0
9x 1
2. 2
x  x  20
x  x  20  0
2
( x  5( x  4  0
x 5  0 x  4  0
5 5 4 4
x 5
x  4
3.8
Simplify Rational Expressions
Example 2 Simplify expressions by dividing out monomials
Simplify the rational expression, if possible. State the
excluded values.
18 x

x

3
6
a.

2
6x
6 x  x
6x  0
2
6
6
x 0
2
3

x
The excluded value is _____.
0
x0
Simplify Rational Expressions
3.8
Example 2 Simplify expressions by dividing out monomials
Simplify the rational expression, if possible. State the
excluded values.
6 x(2 x  1
6 4  x
 x(2 x  1
6

6 4  x
2
x

1

4
12 x  6 x

b.
24 x
2
The excluded value is _____.
0
24x  0
24 24
x0
3.8
Simplify Rational Expressions
Checkpoint. Simplify the rational expression, if
possible. State the excluded values.
7
3.
5x  3
Since the expression on the top and bottom
cannot be factored, and they do not have any
common factors other than 1, the expression is
already simplified.
5x  3  0
3 3
5x  3
5
5
3
x
5
3.8
Simplify Rational Expressions
Checkpoint. Simplify the rational expression, if
possible. State the excluded values.
5x
5

x
x
4. 2


2
2
x 5
5 x  25
5( x  5 
5 x  25  0
 25  25
2
5x  25
5
5
2
x 5
x 5
2
Simplify Rational Expressions
3.8
Checkpoint. Simplify the rational expression, if
possible. State the excluded values.
3
6x

5.
2x  4
2x  4  0
44
2 x  4
2
2
x  2
2  3 x
2( x  2
3
3
3x

x2
3.8
Simplify Rational Expressions
Example 3 Simplify expressions by dividing out binomials
x 2  x  12
Simplify 2
. State the excluded values.
x  5x  6
x  x  12 (x  4( x  3

2
x  5 x  6 ( x  3( x  2
2
x

4

x2
(x  3(x  2  0
x 3  0 x  2  0
3 3 2 2
x3
x2
The excluded values are _____
3 and _____.
2
Simplify Rational Expressions
3.8
Checkpoint. Simplify the rational expression, if
possible. State the excluded values.
x  7 x  6 (x  6(x  1
x

1


6. 2
x 3
x  3x  18 (x  6(x  3
2
(x  6(x  3  0
x  6  0 x 3  0
3 3
6 6
x  6
x 3
Simplify Rational Expressions
3.8
Checkpoint. Simplify the rational expression, if
possible. State the excluded values.
(

 x 4
(
x  2(x  2
x

2


7. 2
x7
( x  7  ( x  2
x  5 x  14
2
(x  7(x  2  0
x7  0 x2  0
7 7 2 2
x  7
x2
3.8
Simplify Rational Expressions
Pg. 178, 3.8 #1-21