For which of the following values of x x is the rational expression undefined? x + 1 x 2 − 9 \frac{x+1}{x^2-9}

This problem asks for which of the following values of x is the rational expression undefined. Now notice we have x plus one over x squared minus nine. When it comes to these rational expressions, we cannot have zero in the denominator. So x squared minus nine equaling zero would be where the rational expression is undefined. So what I'll do is solve for x by adding nine on both sides of this equation. That gets the nines to cancel, giving me that x squared is equal to positive nine. Now Now at this point, what I need to do is take the square root on both sides of the equation. That cancels the square and the square root, giving me just x. And then the square root of nine, well, this is gonna give me plus or minus three. We get a positive and a negative because that's what happens when you take the square root on both sides of the equation. So we cannot have x as positive three or negative three, because if x equals either of these values, then the rational expression will be undefined. Hope you found this video helpful.

8. Rational Expressions and Equations

Simplifying Rational Expressions

Beginning & Intermediate Algebra

8. Rational Expressions and Equations

Simplifying Rational Expressions

Struggling with Beginning & Intermediate Algebra?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

For which of the following values of $x$ is the rational expression undefined?
$\frac{x + 1}{x^{2} - 9}$

$0$

$\pm3$

$\pm9$

$\pm1$

Verified step by step guidance

Identify when a rational expression is undefined: it is undefined when its denominator is equal to zero.

Set the denominator equal to zero: $x^2 - 9 = 0$.

Recognize that $x^2 - 9$ is a difference of squares, which factors as $(x - 3)(x + 3)$.

Set each factor equal to zero to find the values of $x$ that make the denominator zero: $x - 3 = 0$ and $x + 3 = 0$.

Solve each equation to find $x = 3$ and $x = -3$, which are the values for which the rational expression is undefined.

4:37m

Watch next

Master Intro To Rational Expressions with a bite sized video explanation from Patrick Ford

Start learning

Struggling with Beginning & Intermediate Algebra?

For which of the following values of xx is the rational expression undefined?x+1x2−9\frac{x+1}{x^2-9}

Watch next

For which of the following values of $x$ is the rational expression undefined?
$\frac{x + 1}{x^{2} - 9}$