Simplifying a rational expression by factoring

The video tutorial addresses an algebraic expression, X^2 - 4 / X - 2 * X + 1, and explores the challenges in simplifying it. The instructor explains that the expression cannot be simplified using basic exponent rules but can be factored using the difference of two squares method. By rewriting X^2 - 4 as (X - 2)(X + 2), the expression is simplified to X + 2 / X + 1 after canceling out common terms. The tutorial emphasizes the importance of recognizing factoring opportunities in algebraic expressions.

What is the expression that needs to be factored in the problem discussed?

Can you explain why the expression X^2 - 4 can be factored?

What is the factored form of X^2 - 4?

After factoring, what expression do we get when we rewrite the problem?

What is the final answer after simplifying the expression?