Question

the following rational equation has denominators that contain variables. for this equation, a. write the value or values of the variable that make a denominator zero. then use the number line on the next & keeping the restrictions in mind, solve the equation
\\(\frac{4}{5x + 20} = \frac{8}{x + 4} - \frac{3}{5}\\)

a. what is(are) the value or values of the variable that make(s) the denominators zero?
x = \\(\square\\)
(simplify your answer. use a comma to separate answers as needed.)

Explanation:

Step1: Analyze denominators

The denominators are \(5x + 20\) and \(x + 4\). First, simplify \(5x + 20\) as \(5(x + 4)\). So the denominators are \(5(x + 4)\) and \(x + 4\).

Step2: Find values that make denominators zero

Set each denominator equal to zero. For \(x + 4 = 0\), solving gives \(x=-4\). For \(5(x + 4)=0\), dividing both sides by 5 gives \(x + 4 = 0\), so also \(x=-4\).

Answer:

\(x = -4\)