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{2}{x + 2}+5 = \frac{17}{x + 2}\\)

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: Identify denominators

The denominators in the equation \(\frac{2}{x + 2}+5=\frac{17}{x + 2}\) are \(x + 2\) (appearing twice).

Step2: Set denominator to zero

To find the value of \(x\) that makes the denominator zero, we solve the equation \(x+2 = 0\).

Step3: Solve for x

Subtract 2 from both sides of the equation \(x + 2=0\), we get \(x=-2\).

Answer:

\(-2\)