Question

without actually solving the equation, list all possible numbers that would have to be rejected if they appeared as potential solutions. \\(\frac{1}{2x} + \frac{1}{5x} = \frac{x}{5}\\) select the correct choice below and, if necessary, fill in the answer box to complete your choice. \\(\bigcirc\\) a the solutions cannot include \\(\square\\) (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 Denominators

The equation is $\frac{1}{2x}+\frac{1}{5x}=\frac{x}{5}$. The denominators are $2x$, $5x$, and 5 (but 5 has no variable, so focus on $2x$ and $5x$).

Step2: Find Values to Reject

For a fraction $\frac{a}{b}$, $b
eq0$. So set $2x = 0$ and $5x = 0$. Solving both gives $x = 0$. So $x = 0$ must be rejected as a potential solution because it makes the denominators $2x$ and $5x$ equal to zero, which is undefined in rational expressions.

Answer:

A. The solutions cannot include $0$