63: Complex Rational Expressions

1
6-3 Complex Rational Expressions
complex rational expression (fraction) contains
a fraction in its numerator, denominator, or both.
2
Method 1 Find LCD of all denominators, then
multiply both the numerator and denominator by
the LCD.
Ex 1
Multiply numerator and denominator by LCD
LCD y
y
Distribute ?
?
y
3
Ex 2

• LCD

Multiply numerator and denominator by LCD
Distribute ?
?
factor ?
4
Ex 3

• LCD

Multiply numerator and denominator by LCD
Distribute ?
?
Factor ?
5
Ex 4
LCD

• Rewrite with positive
• exponents

?
Multiply numerator and denominator by LCD
Distribute ?
?
factor ?
6
Ex 5

• LCD

Multiply numerator and denominator by LCD
Distribute ?
?
7
Method 2 Simplify the numerator and denominator
separately, then use division and multiply by
reciprocal.
Add fractions in numerator and denominator.
Ex 6
LCD
Multiply by reciprocal
?
?
8
Ex 7
Simplify the numerator and denominator
Factor ?
?
Multiply by reciprocal
?
?
9
Ex 8
Simplify the numerator and denominator
Factor ?
?
Multiply by reciprocal
?
?
10
Ex 9
Simplify the numerator and denominator
Factor ?
?
Multiply by reciprocal
?
?
11
6-3 Summary

• Method 1 Find LCD of all denominators, then
• multiply both the numerator and denominator by
  the
• LCD.

?
?
Method 2 Simplify the numerator and denominator
separately, then use division and multiply by
reciprocal.
?
?
?
?