-6x+9/2xy-3y

To simplify the expression \(-\frac{6x + 9}{2xy - 3y}\), we will first factor both the numerator and the denominator where possible. 1. **Factor the numerator:** The numerator is \(-6x + 9\). We can factor out a -3: \[ -6x + 9 = -3(2x - 3) \] 2. **Factor the denominator:** The denominator is \(2xy - 3y\). We can factor out a \(y\): \[ 2xy - 3y = y(2x - 3) \] 3. **Rewriting the expression:** Now substituting the factored forms back into the original expression gives: \[ -\frac{6x + 9}{2xy - 3y} = -\frac{-3(2x - 3)}{y(2x - 3)} \] 4. **Canceling common factors:** The \((2x - 3)\) terms in the numerator and the denominator cancel out, provided that \(2x - 3 \neq 0\): \[ -\frac{-3}{y} = \frac{3}{y} \] Thus, the simplified expression is: \[ \frac{3}{y} \quad \text{(where \(2x - 3 \neq 0\))} \]