Find the Domain for the Function: (2x+2)/(3x-1)

To find the domain of the function $\frac{2x + 2}{3x - 1}$, we must ensure that the function is defined for all values of $x$ except where the denominator is zero.

Follow these steps to determine the domain:

• Step 1: Identify the denominator of the function. The denominator is $3x - 1$.
• Step 2: Set the denominator equal to zero and solve for $x$: $3x - 1 = 0$
• Step 3: Solve the equation $3x - 1 = 0$: $3x = 1$ $x = \frac{1}{3}$
• Step 4: State the domain. Since the function is undefined at $x = \frac{1}{3}$, the domain consists of all real numbers except $x = \frac{1}{3}$.

The domain of the function $\frac{2x + 2}{3x - 1}$ is therefore all real numbers $x$ such that $x \neq \frac{1}{3}$.

Thus, the solution is: $x \ne \frac{1}{3}$.