Transcript 10-10 Complex Rational Expressions

10-10
Complex Rational Expressions
Standard
13.0
One Key Term
Vocabulary
1.
Complex rational
expressions
1.
A rational expression
that has a rational
expression in its
numerator or
denominator or
both.
What is the most number of terms in
either the numerator or denominator?
1.
2.
x
x y
x2
2
2
x y
x x2

2 y y 1
2
x
2x  3

y 1
y
1.
One Term
2.
Two Terms
Simplifying Complex Rational Expressions
(At least Two Terms)
 At least two terms in the numerator or
denominator.
a. Find the LCM of the numerator’s fractions and
the denominator’s fractions.
b. Multiply the numerator and the denominator of
the complex rational expression by the LCM.
c. Simplify.
Simplifying Complex Rational Expressions
(One Term Only)
One term only in both the numerator and
denominator of the complex rational
expression.

1.
2.
Write the complex rational expression out by
replacing a division by a product of the
reciprocal.
Factor, simplify, and multiply.
#3 Simplify.
x x

2 3
1
2
 x x
6  
2 3 
1
6 
2
LCM  6
3x  2 x

3
5x
3
#4 Simplify.
1 LCM  x 2
1
x 
1
1 2
x
 1
x 1  
2
x
x
x( x  1)
 x 


2
1 
x 1
( x  1)(x  1)
2
x 1  2 
 x 
2
x
x 1
#5 Simplify.
3
(t  2)(2t  1)

t
t2
3
t


(t  2)(2t  1) t  2
3
t2


(t  2)(2t  1)
t
3
t (2t  1)
#6 Simplify.
5 3

3 4 
1 2

2 3
LCM  12
5 3
12  
3 4 
1 2
12  
2 3
20  9

68
29
14