Questions: For what value of (x) is the rational expression below equal to zero? ((20+2x)/(5-x)) A. -5 B. 10 C. -10 D. 5

For what value of (x) is the rational expression below equal to zero? ((20+2x)/(5-x)) A. -5 B. 10 C. -10 D. 5
Transcript text: Window Help course.apexlearning.com Apex Learning 1.2.3 Quiz: Rational Expressions Question 10 of 10 For what value of $x$ is the rational expression below equal to zero? \[ \frac{20+2 x}{5-x} \] A. -5 B. 10 C. -10 D. 5 SUBM - PREVIOUS
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Solution

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Solution Steps

Step 1: Understand the problem

We are tasked with finding the value of \( x \) that makes the rational expression equal to zero: \[ \frac{20+2x}{5-x} = 0 \] A rational expression equals zero when its numerator is zero (and its denominator is not zero).

Step 2: Set the numerator equal to zero

Set the numerator \( 20 + 2x \) equal to zero and solve for \( x \): \[ 20 + 2x = 0 \] \[ 2x = -20 \] \[ x = -10 \]

Step 3: Verify the denominator is not zero

Ensure that the denominator \( 5 - x \) is not zero for \( x = -10 \): \[ 5 - (-10) = 15 \neq 0 \] Since the denominator is not zero, \( x = -10 \) is a valid solution.

Final Answer

The value of \( x \) that makes the rational expression equal to zero is: \[ \boxed{x = -10} \] The correct choice is C.

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