How to simplify rational expressions? A tutorial with examples and detailled solutions is presented.

To simplify a rational expression, we first factor both the numerator and denominator completely then reduce the expression by cancelling common factors.

Example 1: Simplify the rational expression

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.