Question
Find all excluded values for the expression. That is, find all values of \( v \) for which the expression is undefined. \( \frac{v-4}{v^{2}-36} \) If there is more than one value, separate them with commas. \( v=\square \)
Ask by Newton Harmon. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
v = 6, -6
Solution
To determine the excluded values, set the denominator equal to zero and solve for v.
Denominator: v² - 36 = 0
Factor the denominator: (v - 6)(v + 6) = 0
Set each factor equal to zero:
v - 6 = 0 ⇒ v = 6
v + 6 = 0 ⇒ v = -6
Thus, the expression is undefined when v = 6 or v = -6.
v = 6, -6
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Simplify this solution Beyond the Answer
To find the excluded values for the expression \(\frac{v-4}{v^{2}-36}\), we need to determine when the denominator is equal to zero since division by zero is undefined. The denominator is \(v^{2} - 36\), which can be factored as \((v - 6)(v + 6)\). Setting the denominator equal to zero gives us: \[ (v - 6)(v + 6) = 0 \] This results in two solutions: \[ v - 6 = 0 \quad \Rightarrow \quad v = 6 \] \[ v + 6 = 0 \quad \Rightarrow \quad v = -6 \] Thus, the excluded values for the expression are \(v = 6, -6\). So, the final answer is: \( v=6, -6 \)
