1Cademy - Finding Undefined Values of $$\frac{8a^2b}{3c}$$, $$\frac{4b-3}{2b+5}$$, and $$\frac{x+4}{x^2+5x+6}$$

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Finding Undefined Values of $\frac{8a^2b}{3c}$ , $\frac{4b-3}{2b+5}$ , and $\frac{x+4}{x^2+5x+6}$

To determine the values for which each rational expression is undefined, set the denominator equal to zero and solve for the variable.

ⓐ $\frac{8a^2b}{3c}$ : The denominator is $3c$ . Setting it equal to zero gives $3c = 0$ , which yields $c = 0$ . Thus, the expression is undefined for $c = 0$ .

ⓑ $\frac{4b - 3}{2b + 5}$ : The denominator is $2b + 5$ . Set it equal to zero and solve: $2b + 5 = 0$ $2b = -5$ $b = -\frac{5}{2}$ Thus, the expression is undefined for $b = -\frac{5}{2}$ .

ⓒ $\frac{x + 4}{x^2 + 5x + 6}$ : The denominator is $x^2 + 5x + 6$ . Set it equal to zero and factor: $x^2 + 5x + 6 = 0$ $(x + 2)(x + 3) = 0$ $x + 2 = 0 \text{ or } x + 3 = 0$ $x = -2 \text{ or } x = -3$ Thus, the expression is undefined for $x = -2$ or $x = -3$ .

These examples show increasing complexity: a monomial denominator yields a single restricted value directly, a binomial denominator requires solving a two-step linear equation, and a quadratic trinomial denominator requires factoring and applying the Zero Product Property.

Updated 2026-05-14

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