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

MULTIPLICATION AND DIVISION

TO MULTIPLY RATIONAL EXPRESSIONS

  1. Factor the numerators and the denominators of each fraction.
  2. Cancel out common factors in pairs(top and bottom only).
  3. Multiply the numerators to get the new numerator and the denominators to get the new denominator.
  4. Note: Place parentheses around factors in order to keep the signs correct.

 

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