Rewriting Fractions: Factoring, Rationalizing, Embedded

1
Rewriting Fractions Factoring, Rationalizing,
Embedded
2
Simplifying Rational Expressions
Can NOT cancel since everything does not have a
common factor and its not in factored form
Simplify
Factor Completely
CAN cancel since the top and bottom have a common
factor
This form is more convenient in order to find the
domain
3
Polynomial Division Area Method
Simplify
Quotient



x3
3x2
-x
-1
Dividend (make sure to include all powers of x)
x
x4
3x3
-x2
-x
The sum of these boxes must be the dividend
Divisor
- 3
-3x3
-9x2
3x
3
x4 0x3 10x2 2x 3
Needed
Needed
Needed
Check
Needed
x3 3x2 x 1
4
Rationalizing Irrational and Complex Denominators
The denominator of a fraction typically can not
contain an imaginary number or any other radical.
To rationalize the denominator (rewriting a
fraction so the bottom is a rational number)
multiply by the conjugate of the denominator.
Ex Rationalize the denominator of each fraction.
a.
b.
5
Simplifying Complex Fractions
To eliminate the denominators of the embedded
fractions, multiply by a common denominator
Simplify
It is not simplified since it has embedded
fractions
No Common Factor. Not everything can be
simplified!
Check to see if it can be simplified more
6
Trigonometric Identities
Simplify
Split the fraction
Use Trigonometric Identities
Write as simple as possible