Detailed Solution to Example 1

• Factor both the numerator and denominator completely.
  
  
  
• Cancel common factors to reduce and simplify the given expression.
  
  
  Note: The given expression is equal to 2 on the condition that x is not equal to 1. x = 1 is not in the domain of the expression.

Example 2: Simplify the rational expression

Detailed Solution to Example 2

• Factor both the numerator and denominator completely.
  
  
  
• Cancel common factors to simplify the expression.
  

Example 3: Simplify the rational expression

Detailed Solution to Example 3

• Factor both the numerator and denominator completely.
  
  
  
• Note that - x + 1 = - (x - 1) in the denominator.
  
  
  
• Cancel common factors.
  

Exercises

Simplify the rational expression.

Answers to the above exercises

• Definition and domain of Rational Expressions.