Question
Find all excluded values for the expression. That is, find all values of \( x \) for which the expression is undefined. \[ \frac{3 x}{4 x+8} \] If there is more than one value, separate them with commas.
Ask by Sullivan Warner. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression is undefined when \( x = -2 \).
Solution
1. Set the denominator equal to 0:
\[
4x + 8 = 0
\]
2. Subtract 8 from both sides:
\[
4x = -8
\]
3. Divide both sides by 4:
\[
x = -2
\]
Thus, the expression is undefined when \( x = -2 \).
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Simplify this solution Bonus Knowledge
To find the excluded values for the expression \( \frac{3 x}{4 x + 8} \), we need to determine when the denominator is equal to zero because a fraction is undefined when its denominator is zero. Set the denominator equal to zero: \[ 4x + 8 = 0 \] Now, solve for \( x \): 1. Subtract 8 from both sides: \[ 4x = -8 \] 2. Divide both sides by 4: \[ x = -2 \] Thus, the only excluded value for the expression is \( -2 \).
