Download H. Algebra 2 9.4 notes – Rational Expressions Warm Up: Evaluate. 1

H. Algebra 2
9.4 notes – Rational Expressions
Warm Up: Evaluate.
2 3
1.  =
3 7
4 5
=

9 12

3.

Factor each expression.
5. x 2  81


2.
3 8
=

4 15
4.
9 3
=

10 10
6. x 2 16x  36


Simplifying Rational Expressions.
To simplify a rational expression, divide the numerator and the denominator by a common factor.
Simplify
x 2  5x  6
=
x 2  36

Simplify
b 2  49
=
b 2  8b  7

Multiplying Rational Expressions.
It’s just like multiplying fractions!
Simplify
3 4 x 3 14
=


4 x 2 21 4 x 5

Simplify

Simplify
28 4a 5
3
=


3
4a 21 49a 4

x 1
x2  x  6
=

x 2  2x  3 x 2  2x  3
Simplify
x 2  25
x2  4

=
x 2  5 x  6 x 2  2 x  15
Simplify
x 2  4 x 12 x 2  2x  35
=

x 2  11x  30
x4

Simplify
x2  4x  5
x2  4
=

x 2  3x  2 x 2  3x 10

Dividing Rational Expressions.
…Same as fraction rules!
6 12
Simplify 3  5 =
x
x
2r 2 2s2
Simplify 2rs 
=

s
r


Simplify
x 2  25
x5
=
 2
2
x  2x  3 x  3x 18

Simplify

Simplify
x4
x 2  3x  4

=
(x  2) 2
x2  4

2x 2  2x x 2  x  2
=
 2
x2  9
x  2x  3
Simplify

4 x 2  20x
x5
=
 2
2
x  6x  9 x  9
Complex Fractions
A complex fraction is a quotient that contains one or more fractions in the numerator, the denominator,
or both.
4a 2 1
2
Simplify the complex fraction a  4 =
2a 1
a2

(x  2) 2
Simplify the complex fraction x2  3 =
x 4
(x  3) 2

b2  4
2
Simplify the complex fraction b  2b  1 =
b2
b 1

x2  4x  3
2
Simplify the complex fraction x2  6x  8 =
x  9x  18
x 2  7x  10

Practice:
Simplify each expression.
x2
x2 x2

1.
=
x  5 x 1
x5

1
x
2. x 2 3 
=
x
x7
x7

x3
4. x  1 1 =
x(x 1)
x
2x  3
 x 1 =
3.
3x
x 1
2x  3


5.
3x 3 6 y 5
=

5 y 2 4x5
6. x 2  5 x  6 
x 2  3x  2
x2  2x  3