Question

what values of the variable cannot possibly be solutions for the given
\\(\frac{7}{3x + 2}-\frac{1}{x - 5}=0\\)

select the correct choice below and, if necessary, fill in the answer box
a.
the solutions cannot include \\(\frac{37}{4}\\)
(simplify your answers. type an integer or a fraction. use a com
b. there are no numbers that would have to be rejected as potenti

Explanation:

Step1: Identify undefined denominators

Set each denominator equal to 0:
$3x + 2 = 0$
$x - 5 = 0$

Step2: Solve for x (first denominator)

Isolate x from $3x + 2 = 0$:
$3x = -2 \implies x = -\frac{2}{3}$

Step3: Solve for x (second denominator)

Isolate x from $x - 5 = 0$:
$x = 5$

Answer:

The solutions cannot include $\boldsymbol{-\frac{2}{3}}$ and $\boldsymbol{5}$.

(Note: The provided option A is incorrect, as $\frac{37}{4}$ is the valid solution to the equation, not a value to exclude. Excluded values come from making denominators zero, which are $-\frac{2}{3}$ and $5$.)