Question

what values of the variable cannot possibly be solutions for the given equation, without actually solving the equation
\\(\frac{8}{5x + 3}-\frac{1}{x - 2}=0\\)

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

\\(\bigcirc\\) a. the solutions cannot include \\(\square\\).
(simplify your answers. type an integer or a fraction. use a comma to separate answers as needed.)
\\(\bigcirc\\) b. there are no numbers that would have to be rejected as potential solutions.

Explanation:

Step1: Identify undefined points

For a rational equation, the denominator cannot be zero. So we set each denominator equal to zero and solve for \(x\).
For \(5x + 3 = 0\):
\[

$$\begin{align*} 5x+3&=0\\ 5x&=-3\\ x&=-\frac{3}{5} \end{align*}$$

\]
For \(x - 2 = 0\):
\[
x = 2
\]

Step2: Determine non - solutions

These values of \(x\) (\(-\frac{3}{5}\) and \(2\)) make the denominators zero, so they cannot be solutions of the equation.

Answer:

The solutions cannot include \(-\frac{3}{5}, 2\)