Find the Domain of 65/(2x-2)²: Analyzing Undefined Points

To solve for the domain of the function $\frac{65}{(2x-2)^2}$, follow these steps:

• Step 1: Identify when the denominator $(2x-2)^2$ equals zero because the denominator cannot be zero.
• Step 2: Solve the equation $(2x-2)^2 = 0$. This simplifies to $2x-2 = 0$.
• Step 3: Solve for $x$ by adding 2 to both sides: $2x = 2$.
• Step 4: Divide both sides by 2 to isolate $x$: $x = 1$.
• Step 5: The value $x = 1$ makes the denominator zero, so it must be excluded from the domain.

Thus, the domain of the function is all real numbers except $x \ne 1$.

Therefore, the solution to the problem is $x \ne 1$.