RATIONAL EXPRESSIONS
A rational expression is the quotient of two polynomials.
A rational expression is undefined when its denominator has the value 0.
A SIGN PROPERTY OF RATIONAL EXPRESSIONS
A negative in a fraction may be on the numerator, denominator or
the front of the fraction.
Example 1
Evaluate when y is 2.
Example 2
For what values is the fraction undefined? | Set the denominator =0 and solve. | |
Let 2x-3=0 and solve. |
FUNDAMENTAL PRINCIPLE OF RATIONAL EXPRESSIONS
THE FUNDAMENTAL PRINCIPLE OF RATIONAL EXPRESSIONS
If A, B. and C are polynomials, then where B and C do not have the value 0.
The Fundamental Principle applies only to factors.
Reducing fractions is performed using the Fundamental Principle.
Using the fundamental principle, we reduce rational expressions.
We must factor the numerator and denominator in order to reduce.
REDUCING OPPOSITES
Sometimes we want to change the denominator of a rational expression. If we
reverse the Fundamental Principle to , then we can multiply a fraction
by the same non-zero number C and gain an equivalent fraction. We do this in addition of
fractions.
Examples 1 | |
Example 2 | |
TO MULTIPLY RATIONAL EXPRESSIONS
If A, B, C and D are polynomials where B and D do not have value 0, then
TO DIVIDE RATIONAL EXPRESSIONS
1. Change the problem to multiplication by multiplying by the reciprocal of the divisor. (turn the second fraction upside down)
2. Factor the numerators and the denominators of each fraction.
2. Cancel and then multiply the fractions.
If A, B, C, and D are polynomials where B, C, and C do not have value 0.
Example 1
Example 2
Example 3