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 Algebra

8. Rational Expressions and Equations

Simplifying Rational Expressions

Struggling with Beginning Algebra?

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Multiple Choice

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

$0$

$\pm 3$

$\pm 9$

$\pm 1$

Verified step by step guidance

Identify when a rational expression is undefined: it is undefined when its denominator equals zero because division by zero is not allowed.

Set the denominator equal to zero to find the values of $ x $ that make the expression undefined: $ x^2 - 9 = 0 $.

Recognize that $ x^2 - 9 $ is a difference of squares, which can be factored as $ (x - 3)(x + 3) = 0 $.

Use the zero product property, which states that if $ (x - 3)(x + 3) = 0 $, then either $ x - 3 = 0 $ or $ x + 3 = 0 $.

Solve each equation separately: $ x - 3 = 0 $ gives $ x = 3 $, and $ x + 3 = 0 $ gives $ x = -3 $. These are the values for which the rational expression is undefined.

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

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