Solve the Fraction Equation: Find x in (x²-9)/(x-3) = 0

Resolve:

$\frac{x^2-9}{x-3}=0$

To solve this problem, we'll follow these steps:

• Step 1: Factor the numerator using the difference of squares formula.
• Step 2: Set the factored numerator equal to zero to find potential solutions for $x$.
• Step 3: Ensure none of these solutions result in the denominator being zero.

Now, let's work through each step:
Step 1: The numerator $x^2 - 9$ can be factored as $(x - 3)(x + 3)$.
Step 2: Set the factored numerator to zero: $(x - 3)(x + 3) = 0$.
This gives two potential solutions: $x - 3 = 0$ or $x + 3 = 0$. Solving these equations, we get $x = 3$ or $x = -3$.
Step 3: Verify that these solutions do not result in division by zero:
- For $x = 3$, the denominator $x - 3 = 0$, which means division by zero occurs, so it is not a valid solution.
- For $x = -3$, the denominator $x - 3$ is not zero, as $(-3 - 3) = -6$, hence $x = -3$ is a valid solution.

Therefore, the solution to the problem is $x = -3$.