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. these are the restrictions on the variable. b. keeping the restrictions in mind, solve the equation.

\\(\frac{9}{5x + 25}=\frac{6}{x + 5}-\frac{3}{5}\\)

a. what is/are the value or values of the variable that make(s) the denominators zero?

x =
(simplify your answer. use a comma to separate answers as needed.)

Explanation:

Step1: Set first denominator to zero

Set $5x + 25=0$. Solve for $x$:
\[

$$\begin{align*} 5x+25&=0\\ 5x&=- 25\\ x&=-5 \end{align*}$$

\]

Step2: Set second denominator to zero

Set $x + 5=0$. Solve for $x$:
\[

$$\begin{align*} x+5&=0\\ x&=-5 \end{align*}$$

\]
The third - denominator $5$ is a constant and never zero.

Answer:

$-5$