What value makes the equation −5 = 4−3/x4−3x undefined?(1 point)

Question

What value makes the equation  −5 = 4−3/x4−3x  undefined?(1 point)
Responses

−4/3
negative Start Fraction 4 over 3 End Fraction

−3/4
negative Start Fraction 3 over 4 End Fraction

4/3
Start Fraction 4 over 3 End Fraction

3/4

GPT-4o mini · Answer

To determine when the equation $-5 = \frac{4 - 3}{x^4 - 3x}$ is undefined, we need to analyze the denominator $x^4 - 3x$. The expression is undefined when the denominator equals zero: $$ x^4 - 3x = 0 $$ We can factor out $x$: $$ x(x^3 - 3) = 0 $$ Setting each factor to zero gives us: 1. $x = 0$ 2. $x^3 - 3 = 0 \Rightarrow x^3 = 3 \Rightarrow x = \sqrt[3]{3}$ Thus, the values that make the equation undefined are $x = 0$ and $x = \sqrt[3]{3}$. Now, none of the provided answers $-\frac{4}{3}$, $-\frac{3}{4}$, $\frac{4}{3}$, or $\frac{3}{4}$ are equal to either of those values. Therefore, none of the provided options directly lead to the equation being undefined, since it is undefined at $x = 0$ and $x = \sqrt[3]{3}$. If I need to select only from the provided responses, they do not represent any values that cause the equation to be undefined.

kacey · Answer

whats the answer

GPT-4o mini · Answer

To find out when the expression $-5 = \frac{4 - 3}{x^4 - 3x}$ is undefined, we look at the denominator $x^4 - 3x$. Setting the denominator to zero: $$ x^4 - 3x = 0 $$ Factoring out $x$: $$ x(x^3 - 3) = 0 $$ This gives us two conditions: 1. $x = 0$ 2. $x^3 - 3 = 0 \Rightarrow x = \sqrt[3]{3}$ The values that make the equation undefined cannot be found directly from the provided response options $-\frac{4}{3}$, $-\frac{3}{4}$, $\frac{4}{3}$, or $\frac{3}{4}$. However, if there is a misunderstanding and we are only checking for the responses given, the answer doesn't appear on the list. If you were looking for a match from the list, please clarify, as none of the answers make the original equation undefined based on the calculations provided.