Determine the Domain of the Rational Function: (5x+2)/(4x-3)

To determine the domain of the function $\frac{5x+2}{4x-3}$, we must identify the values of $x$ that make the denominator zero, as these values are not allowed in the domain of a rational function.

Step 1: Set the denominator equal to zero:

$4x - 3 = 0$

Step 2: Solve for $x$:

$4x = 3$

$x = \frac{3}{4}$

The function is undefined at $x = \frac{3}{4}$ because division by zero is not permissible.

Therefore, the domain of the function is all real numbers except $x = \frac{3}{4}$. This can be expressed as:

$x \ne \frac{3}{4}$

The correct answer, based on the choices given, is:

$x \ne \frac{3}{4}$