Simplifying a Rational Expression and Identifying Undefined Values

Very Hard Advanced Math Rational Expressions

Consider the rational expression $$R(x) = \f\frac{2x^2 - 8}{x^2 - 4}.$$ Simplify this expression completely. What values of $$x$$ make the expression undefined?

Given that rational expressions can have restrictions based on their denominators, identify any factorization that might help in simplifying and recognizing the points of discontinuity in the expression.

The expression simplifies to $$2(x + 2)$$, undefined for $$x = 2$$ and $$x = -2$$.

The expression simplifies to $$2$$, undefined for no values of $$x$$.

The expression simplifies to $$\frac{2(x - 2)}{(x - 2)(x + 2)}$$, undefined for $$x = 2$$.

The expression simplifies to $$\frac{2(x^2 - 4)}{(x-2)(x+2)}$$, undefined for $$x = 0$$.

Hint

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