Simplifying Rational Expressions
Comprehensive Study Summary
1. Core Concept
A rational expression is simplified by dividing both the numerator and the
denominator by their Greatest Common Factor (GCF). This is identical to
simplifying numerical fractions (e.g., 12/20 = 3/5).
2. Steps to Simplify
1. Factor: Factor both the numerator and denominator completely.
2. Identify Undefined Values: Determine which values of x make the
original denominator equal to zero.
3. Eliminate: Cancel out the common factors (brackets) that appear in both
top and bottom.
Example:
Expression: (x² + 3x - 4) / (x² - x)
Step 1 (Factoring): [(x - 1)(x + 4)] / [x(x - 1)]
Step 2 (Eliminating): (x - 1) cancels out.
Result: (x + 4) / x
3. Undefined Values
A rational expression is undefined when the denominator equals zero. You
must check this using the denominator before you simplify.
Comprehensive Study Summary
1. Core Concept
A rational expression is simplified by dividing both the numerator and the
denominator by their Greatest Common Factor (GCF). This is identical to
simplifying numerical fractions (e.g., 12/20 = 3/5).
2. Steps to Simplify
1. Factor: Factor both the numerator and denominator completely.
2. Identify Undefined Values: Determine which values of x make the
original denominator equal to zero.
3. Eliminate: Cancel out the common factors (brackets) that appear in both
top and bottom.
Example:
Expression: (x² + 3x - 4) / (x² - x)
Step 1 (Factoring): [(x - 1)(x + 4)] / [x(x - 1)]
Step 2 (Eliminating): (x - 1) cancels out.
Result: (x + 4) / x
3. Undefined Values
A rational expression is undefined when the denominator equals zero. You
must check this using the denominator before you simplify.
