x+3/x+3•y-3/x²-9

To simplify the expression \( \frac{x + 3}{x + 3} \cdot \frac{y - 3}{x^2 - 9} \), follow these steps:

1. Factor where possible:

   • Notice that \( x^2 - 9 \) can be factored as a difference of squares: \[ x^2 - 9 = (x - 3)(x + 3) \]

2. Rewrite the expression: \[ \frac{x + 3}{x + 3} \cdot \frac{y - 3}{(x - 3)(x + 3)} \]

3. Cancel out the common terms: When \( x + 3 \neq 0 \): \[ = 1 \cdot \frac{y - 3}{(x - 3)(x + 3)} \] Thus, the simplified form is: \[ \frac{y - 3}{x - 3} \] for \( x \neq -3 \).

So, the final result is: \[ \frac{y - 3}{x - 3} \quad \text{(for } x \neq -3\text{)} \]