Determining the Domain of the Rational Function: 5+4x/x²

To determine the domain of the function $\frac{5+4x}{x^2}$, we need to identify values of $x$ that cause the denominator to be zero, as the function is undefined for these values.

Step 1: Set the denominator equal to zero:

$x^2 = 0$

Step 2: Solve for $x$:

Taking the square root of both sides gives $x = 0$.

The function is undefined at $x = 0$, so we must exclude this value from the domain.

Thus, the domain of the function is all real numbers except $x = 0$.

The domain can be expressed as: $x \ne 0$.

Therefore, the correct answer is option 3: Yes, $x \ne 0$.